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Thermodynamics An Interactive Approach 1st edition Subrata Bhattacharjee - Solutions

Steam and ammonia are the working fluids in a binary vapor power cycle consisting of two ideal Rankine cycles. The heat rejected from the steam cycle is provided to the ammonia cycle. In the steam cycle, steam at 6 MPa, 650oC enters the turbine and exits at 60oC. Saturated liquid at 60oC enters the
Water and refrigerant R-134a are the working fluids in a binary cycle used for cogeneration of power and process steam. In the steam cycle, superheated vapor enters the turbine with a mass flow rate of 5 kg/s at 4 MPa, 470oC and expands is entropically to 150 kPa. Half of the flow is extracted at
A geothermal resource exists as saturated liquid at 200oC. The geothermal liquid is withdrawn from a production well at a rate of 200 kg/s, and is flashed to a pressure of 500 kPa by an essentially isenthalpic flashing process, where the resulting vapor is separated from the liquid in a separator
Water is the working fluid in a cogeneration cycle. Steam generator provides 280 kg/s of steam at 9 MPa, 500 o C, of which 110 kg/s is extracted between the first and second stages at 1.5 MPa and diverted to a process heating load. Condensate returns from the process heating load at 1 MPa, 120 o C
A large food processing plant requires 3.5 kg/s of saturated or slightly superheated steam at 550 kPa, which is extracted from the turbine of a cogeneration plant. The boiler generates steam at 7 MPa, 540oC at a rate of 9 kg/s, and the condenser pressure is 14 kPa. Steam leaves the process heater
Consider a cogeneration plant. Steam enters the turbine at 8 MPa and 600oC. 20% of the steam is extracted before it enters the turbine and 60% of the steam is extracted from the turbine at 500 kPa for process heating . The remaining steam continues to expand to 6 kPa. Steam is then condensed at
Repeat problem 9-2-4 [OUW] to determine (a) the maximum rate at which process heat can be supplied.
Steam is generated in the boiler of a cogeneration plant at 4 MPa and 480oC at a rate of 7 kg/s. The plant is to produce power while meeting the process steam requirements for a certain industrial application. One-third of the steam leaving the boiler is throttled to a pressure of 820 kPa and is
Consider a cogeneration power plant modified with regeneration. Steam enters the turbine at 5 MPa, 450oC and expands to a pressure of 0.6 MPa. At this pressure, 65% of the steam is extracted from the turbine, and the remainder expands to 10 kPa. Part of the extracted steam is used to heat the feed
Consider a cogeneration power plant modified with regeneration. Steam enters the turbine at 7 MPa, 440oC at a rate of 20 kg/s and expands to a pressure of 0.4 MPa. At this pressure 60% of the steam is extracted from the turbine, and the remainder expands to 10 kPa. Part of the extracted steam is
The gas-turbine portion of a combined gas-steam power plant has a pressure ratio of 15. Air enters the compressor at 300 K and 1 atm at a rate of 13 kg/s and is heated to 1500 K in the combustion chamber. The combustion gases leaving the gas turbine are used to heat the steam to 400oC at 10 MPa in
Consider a steam power plant operating on the simple ideal Rankine cycle. Steam enters the turbine at 4 MPa, 400oC and is condensed in the condenser at a pressure of 100 kPa. The mass flow rate is 10 kg/s. If the boiler receives heat from a source at 1200oC and the condenser rejects heat to a
Steam is the working fluid in an ideal Rankine cycle. Saturated vapor enters the turbine at 10 MPa and saturated liquid exits the condenser at a pressure of 0.01 MPa. The net power output (W⋅ net) of the cycle is 150 MW. The turbine and the pump both have an isentropic efficiency of 85%. If the
In a steam power plant operating on the ideal regenerative Rankine cycle with one open feed water heater, steam enters the turbine at 9 MPa, 480oC and is condensed in the condenser at a pressure of 7 kPa. Bleeding from the turbine to the FWH occurs at 0.7 MPa. The net power output (W⋅ net) of the
Repeat problem 9-3-3 [OXP], assuming no steam is bled from the turbine for regeneration.
Water is the working fluid in a cogeneration cycle that generates electricity and provides heat for campus buildings. Steam at 2.5 MPa, 320oC and a mass flow rate (m⋅) of 1 kg/s, expands through a two-stage turbine. Steam at 0.2 MPa with a mass flow rate (m⋅) of 0.3 kg/s is extracted between
A Carnot vapor refrigeration cycle uses R-134a as the working fluid. The refrigerant enters the condenser as saturated vapor at 30oC and leaves as saturated liquid. The evaporator operates at a temperature of -5oC. Determine, in kJ per kg of refrigerant flow, (a) The heat transfer to the
An ideal vapor-compression refrigeration cycle operates at steady state with Refrigerant R-134a as the working fluid. Saturated vapor enters the compressor at -5oC, and saturated liquid leaves the condenser at 35oC. The mass flow rate of refrigerant is 5 kg/min. Determine (a) The compressor power
A large refrigeration plant is to be maintained at -18oC, and it requires refrigeration at a rate of 200 kW. The condenser of the plant is to be cooled by liquid water, which experiences a temperature rise of 8oC as it flows over the coils of the condenser. Assuming the plant operates on the ideal
An ideal vapor-compression refrigeration system operates at steady state with Refrigerant R-12 as the working fluid. Superheated vapor enters the compressor at 25 lbf/in2, 10oF and saturated liquid leaves the condenser at 200 lbf/in2. The refrigeration capacity is 5 tons. Determine (a) The
Refrigerant R-12 enters the compressor of an ideal vapor-compression refrigeration system as saturated vapor at -10oC with a volumetric flow rate of 1 m3/min. The refrigerant leaves the condenser at 35oC and 10 bar. Determine (a) The compressor power, in kW, (b) The refrigerating capacity in tons
A refrigerator using R-134a as the working fluid operates on an ideal vapor compression refrigeration cycle between 0.15 MPa and 1 MPa. If the mass flow rate is 1 kg/s, determine (a) the net power necessary to run the system and (b) the COPR. (c) What-if Scenario: What would the COP be if the
A vapor-compression refrigeration system, using ammonia as the working fluid, has evaporator and condenser pressures of 1 bar and 14 bar, respectively. The refrigerant passes through the evaporator with a negligible pressure drop. At the inlet and exit of the compressor, the temperatures are -12oC
A vapor-compression refrigeration system, with a capacity of 15 tons, has superheated Refrigerant R-134a vapor entering the compressor at 15oC, 4 bar and exiting at 12 bar. The compression process can be taken as polytrophic, with n = 1.01. At the condenser exit, the pressure is 11.6 bar and the
An ideal vapor-compression refrigeration cycle, with ammonia as the working fluid, has an evaporator temperature of -25oC and a condenser pressure of 20 bar. Saturated vapor enters the compressor, and saturated liquid exits the condenser. The mass flow rate of the refrigerant is 3 kg/min. Determine
Refrigerant R-22 is the working fluid in a Carnot vapor refrigeration cycle for which the evaporator temperature is 0°C. Saturated vapor enters the condenser at 40°C, and saturated liquid exits at the same temperature. The mass flow rate of refrigerant is 4 kg/min. Determine (a) The rate of heat
Consider a 500 kJ/min refrigeration system that operates on an ideal vapor-compression refrigeration cycle with refrigerant-134a as the working fluid. The refrigerant enters the compressor as saturated vapor at 150 kPa and is compressed to 800 kPa. (a) Show the cycle on a T-s diagram with respect
Refrigerant R-12 enters the compressor of a refrigerator as superheated vapor at 0.14 MPa, -20oC at a rate of 0.04 kg/s, and leaves at 0.7 MPa, 50oC. The refrigerant is cooled in the condenser to 24oC, 0.65 MPa and is throttled to 0.15 MPa. Disregarding any heat transfer and pressure drops in the
Refrigerant R-12 enters the compressor of a refrigerator at 140 kPa, -10oC at a rate of 0.3 m3/min and leaves at 1 MPa. The compression process is isentropic. The refrigerant enters the throttling valve at 0.95 MPa, 30oC and leaves the evaporator as saturated vapor at -18.5oC. (a) Show the cycle on
A vapor-compression refrigeration system for a household refrigerator has a refrigerating capacity of 1500 Btu/h and uses R-12 as the refrigerant. The refrigerant enters the evaporator at 21.422 lbf/in2 and exits at 5oF. The isentropic compressor efficiency is 70%. The refrigerant condenses at
The refrigerator-freezer unit, shown in the schematic below, uses R-134a as the working fluid and operates on an ideal vapor-compression cycle. The temperatures in the condenser, refrigerator, and freezer are 25oC, 2oC, and -20oC, respectively. The mass flow rate of the refrigerant is 0.1 kg/s. If
Refrigerant-134a is the working fluid in a vapor-compression refrigeration system with two evaporators. The system uses only one compressor. Saturated liquid leaves the condenser at 11 bar, one part of the liquid is throttled to 3 bar, the second part is throttled to the second evaporator at a
An ideal vapor-compression cycle uses R-134a as a working fluid and operates between the pressures of 0.1 MPa and 1.5 MPa. The refrigerant leaves the condenser at 30oC and the heat exchanger at 10oC. The refrigerant is then throttled to the evaporator pressure. Refrigerant leaves the evaporator as
Repeat problem 10-1-26 [OCX] with R-12 as the working fluid.Problem 10-1-26An ideal vapor-compression cycle uses R-134a as a working fluid and operates between the pressures of 0.1 MPa and 1.5 MPa. The refrigerant leaves the condenser at 30oC and the heat exchanger at 10oC. The refrigerant is then
Consider a two-stage R-12 refrigeration system operating between 0.15 MPa and 1 MPa. The refrigerant leaves the condenser as saturated liquid and is throttled to a flash chamber operating at 0.4 MPa. The vapor from the flash chamber is mixed with the refrigerant leaving the low-pressure compressor
Repeat problem 10-1-28 [OCV] with R-134a as the working fluid.Problem 10-1-28Consider a two-stage R-12 refrigeration system operating between 0.15 MPa and 1 MPa. The refrigerant leaves the condenser as saturated liquid and is throttled to a flash chamber operating at 0.4 MPa. The vapor from the
A Carnot vapor refrigeration cycle operates between thermal reservoirs at 40oF and 100oF. For (a) R-12, (b) R-134a, (c) water, (d) R-22 and (e) ammonia as the working fluid, determine the operating pressures in the condenser and evaporator, in lbf/in2, and the coefficient of performance.
Consider an ideal two-stage refrigeration system that uses R-12 as the working fluid. Saturated liquid leaves the condenser at 40oC and is throttled to -20oC. The liquid and vapor at this temperature are separated, and the liquid is throttled to the evaporator temperature at -70oC. Vapor leaving
Consider a two-stage compression refrigeration system operating between the pressure limits of 1.2 MPa and 0.08 MPa. The working fluid is R-12. The refrigerant leaves the condenser as saturated liquid with a mass flow rate of 1 kg/s and is throttled to a flash chamber operating at 0.4 MPa. Part of
A two-stage compression refrigeration system operates between the pressure limits of 1 MPa and 0.12 MPa. The refrigerant, R-134a, leaves the condenser as saturated liquid and is throttled to a flash chamber operating at 0.7 MPa. The refrigerant leaving the low-pressure compressor at 0.7 MPa is also
Consider a two-stage cascade refrigeration system operating between the pressure limits of 2 MPa and 0.05 MPa. Each stage operates on an ideal vapor-compression refrigeration cycle with R-134a as the working fluid. Heat rejection from the lower cycle to the upper cycle takes place in an adiabatic
Consider a two-stage cascade refrigeration system operating between -80oC and 80oC. Each stage operates on an ideal vapor-compression refrigeration cycle. Upper cycle use R-12 as working fluid, lower cycle use R-13. In the lower cycle refrigerant condenses at 0oC, in the upper cycle refrigerant
Consider a two-stage cascade refrigeration system operating between 0.1 MPa and 1 MPa. Each stage operates on the ideal cycle with R-134a as the working fluid. Heat rejection from the lower to the upper cycle occurs at 0.4 MPa. If the mass flow rate in the upper cycle is 0.1 kg/s, determine (a) the
Consider a two-stage cascade refrigeration system operating between -60oC and 50oC. Each stage operates on an ideal vapor-compression refrigeration cycle. The upper cycle uses R-134a as working fluid, lower cycle uses R-22. In the lower cycle refrigerant condenses at 10oC, in the upper cycle
A Carnot vapor refrigeration cycle is used to maintain a cold region at 0oF where the ambient temperature is 75oF. Refrigerant R-134a enters the condenser as saturated vapor at 100 lbf/in2 and leaves as saturated liquid at the same pressure. The evaporator pressure is 20 lbf/in2. The mass flow rate
A steady-flow Carnot refrigeration cycle uses refrigerant-134a as the working fluid. The refrigerant changes from saturated vapor to saturated liquid at 30oC in the condenser as it rejects heat. The evaporator pressure is 120 kPa. (a) Show the cycle on a T-s diagram relative to saturation lines,
Refrigerant R-134a enters the condenser of a steady-flow Carnot refrigerator as a saturated vapor at 100 psia, and it leaves as saturated liquid. The heat absorption from the refrigerated space takes place at a pressure of 30 psia and the mass flow rate is 1 kg/s. (a) Show the cycle on a T-s
A refrigerator uses R-12 as the working fluid operates on an ideal vapor compression refrigeration cycle between 0.15 MPa and 1 MPa. If the mass flow rate is 0.04 kg/s, determine The tonnage of the system, The COPR. Compressor power and
A refrigerator uses R-134a as the working fluid and operates on an ideal vapor-compression refrigeration cycle between 0.15 MPa and 1 MPa. For a cooling load of 10 kW, determine the mass flow rate of the refrigerant through the evaporator.
Refrigerant R-134a enters the compressor of an ideal vapor-compression refrigeration system as saturated vapor at -10oC and leaves the condenser as saturated liquid at 35oC. For a cooling capacity of 20 kW, determine (a) The coefficient of performance (COPR). (b) The mass flow rate, (c) The
In a gas refrigeration system air enters the compressor at 10oC, 50 kPa and the turbine at 50oC, 250 kPa. The mass flow rate is 0.08 kg/s. Assuming variable specific heat, determine (a) The rate of cooling, (b) The net power input and (c) The COP.
Air enters the compressor of an ideal Brayton refrigeration cycle at 120 kPa and 275 K. The compressor pressure ratio is 3, and the temperature at the turbine inlet is 325 K. Treating air as a perfect gas, determine (a) The refrigeration capacity per unit mass of air flow, in kJ/kg and (b) The
A gas refrigeration system uses helium as the working fluid operates with a pressure ratio of 3.5. The temperature of the helium is -10oC at the compressor inlet and 50oC at the turbine inlet. Assuming an adiabatic efficiency of 80% for both the compressor and the turbine, determine (a) The
In problem 10-2-9 [OVI] consider that the compressor and turbine each has an isentropic efficiency of 85%. Determine for the modified cycle, (a) The mass flow rate of air, in lb/s and (b) The coefficient of performance (COPR).
In 10-2-10 [OVL] consider that the compressor and turbine have isentropic efficiencies of 80% and 90%, respectively. Determine for the modified cycle, (a) The coefficient of performance and (b) The irreversibility rates, per unit mass of air flow, in the compressor and turbine, each in kJ/kg, for
A gas refrigeration cycle with a pressure ratio of 3 uses helium as the working fluid. The temperature of the helium is -15oC at the compressor inlet at 50oC at the turbine inlet. Assuming adiabatic efficiencies of 85% for both the turbine and the compressor, determine (a) The minimum temperature
An ideal gas refrigeration system with a regenerative HX uses air as the working fluid. Air enters the compressor at 270 K, 150 kPa at a flow rate of 0.1 m3/min and exits at 400 kPa. Compressed air enters the regenerative HX at 300 K and is cooled down to 270 K as the turbine inlet. Determine (a)
A gas refrigeration system uses air as the working fluid has a pressure ratio of 4. Air enters the compressor at -7oC. The high-pressure air is cooled to 30oC by rejecting heat to the surroundings. It is further cooled to -15oC by regenerative cooling before it enters the turbine. Assuming both the
Helium undergoes a Stirling refrigeration cycle, which is a reverse Stirling power cycle. At the beginning of isothermal compression helium is at 100 kPa, 275 K. The compression ratio is 4 and during isothermal expansion the temperature is 150 K. Determine per kg of helium, (a) the net work per
In an ideal Brayton refrigeration cycle air enters the compressor at 100 kPa and 300 K. The compression ratio is 4, and air enters the turbine inlet at 350 K. The mass flow rate of air is 0.05 kg/s. Determine (a) The rate of cooling, (b) The net power input, (c) The COP, and (d) The Carnot COP.
Air enters the compressor of a perfect-gas refrigeration cycle at 45oF, 10 psia and the turbine at 120oF, 30 psia. The mass flow rate of air through the cycle is 0.5 lbm/s. Determine (a) The rate of refrigeration, (b) The net power input and (c) The coefficient of performance (COPR).
Air enters the compressor of a perfect-gas refrigeration cycle at 15oC, 50 kPa and the turbine at 50oC, 300 kPa. The mass flow rate through the cycle is 0.25 kg/s. Assuming constant specific heats for air (PG model), determine (a) The rate of refrigeration, (b) The net power input and (c) The
Air enters the compressor of an ideal Brayton refrigeration cycle at 200 kPa, 270 K, with a volumetric flow rate of 1 m3/s, and is compressed to 600 kPa. The temperature at the turbine inlet is 330 K. Treating air as a perfect gas, determine (a) The refrigeration capacity in kW and tons and (b)
Repeat 10-2-5 [OVE] if the compressor and turbine have an isentropic efficiency of 80%. Problem 10-2-5 Air enters the compressor of an ideal Brayton refrigeration cycle at 200 kPa, 270 K, with a volumetric flow rate of 1 m3/s, and is compressed to 600 kPa. The temperature at the turbine inlet is
An ideal-gas refrigeration cycle uses air as the working fluid to maintain a refrigerated space at -30oC while rejecting heat to the surrounding medium at 30oC. If the pressure ratio of the compressor is 4, determine (a) The maximum and minimum temperatures in the cycle, (b) The coefficient of
In an ideal Brayton refrigeration cycle air enters the compressor at 18 lbf/in2 and 400oR. The compression ratio is 5, and air enters the turbine inlet at 600oR. The mass flow rate of air is 2 lb/min. Determine: (a) The refrigeration capacity in tons, (b) The net power input in Btu/min, and (c)
An ideal Brayton refrigeration cycle has a compressor pressure ratio of 6. At the compressor inlet, the pressure and temperature of the entering air are 55 lbf/in2 and 600oR. The temperature at the exit of the turbine is 370oR. For a refrigerating capacity of 15 tons, determine (a) The specific
A refrigerator uses R-134a as the working fluid and operates on an ideal vapor compression refrigeration cycle between 0.15 MPa and 1 MPa. A temperature difference of 5°C is maintained for effective heat exchange between the refrigerant and its surroundings at the evaporator and condenser. The
A vapor-compression refrigeration system circulates R-134a at a rate (m) of 10 kg/min. The refrigerant enters the compressor at - 10oC, 1.2 bar and exits at 7 bar. The isentropic compressor efficiency is 68%. There are no significant pressure drops as the refrigerant flows through the condenser and
A vapor-compression refrigeration system circulates R-134a at a rate (m) of 10 kg/min. The refrigerant enters the compressor at - 10oC, 1.2 bar and exits at 7 bar. The isentropic efficiency of the adiabatic compressor is 68%. There are no significant pressure drops as the refrigerant flows through
A heat pump which operates on the vapor-compression cycle uses R-134a as the working fluid. Refrigerant enters the compressor at 20 lbf/in2,10oF and is compressed adiabatically to 200 lbf/in2, 180oF. Saturated liquid enters the expansion valve at 200 lbf/in2, 100oF and exits at 20 lbf/in2. The
An ideal vapor-compression refrigeration cycle uses R-134a as a working fluid and operates between 0.1 MPa and 1.5 MPa. The refrigerant leaves the condenser at 30oC and the heat exchanger at 10oC. The refrigerant is then throttled to the evaporator pressure. Refrigerant leaves the evaporator as a
Repeat problem 10-4-5 with the heat exchanger removed. Problem 10-4-5 An ideal vapor-compression refrigeration cycle uses R-134a as a working fluid and operates between 0.1 MPa and 1.5 MPa. The refrigerant leaves the condenser at 30oC and the heat exchanger at 10oC. The refrigerant is then
A heat pump which operates on the ideal vapor-compression cycle with R- 134a is used to transfer heat at a rate of 20 kW to a space maintained at 50oC from outside atmosphere at 0oC. A temperature difference of 5oC is maintained for effective heat exchange between the refrigerant and its
Repeat problem 10-4-7 with the outside atmosphere at 100 kPa and- 5oC. Problem 10-4-7 A heat pump which operates on the ideal vapor-compression cycle with R- 134a is used to transfer heat at a rate of 20 kW to a space maintained at 50oC from outside atmosphere at 0oC. A temperature difference of
Using the Maxwell's relation and the equation of state, determine a relation for the partial of s with respect to v at constant T for the IG model. Verify the relation using TEST at 100 kPa and 300 K.
Steam is throttled from 4.5 MPa and 400oC to 3.5 MPa. Estimate the temperature change (ΔT) of the steam during this process and the average Joule-Thomson coefficient (μJ).
Consider an infinitesimal reversible adiabatic compression or expansion process. By taking s = s(P, v) and using the Maxwell relations, show that for this process Pvk = constant, where k is isentropic expansion exponent defined as k =(v/P)(∂P/∂v)s. Also, show that the isentropic expansion
Consider a mixture of two gases A and B. Show that when the mass fraction xA and xB are known, the mole-fraction can be determined from yA = MB / [MA (1/xA- 1) + MB] and yB = 1 - yA where MA and MB are the molar masses of A and B.
Nitrogen gas at 400 K and 300 kPa behaves as an ideal gas. Estimate the cp and cv of nitrogen at this state.
A system contains oxygen (ideal gas) at 400 K and 100 kPa. As a result of some disturbance, the conditions of the gas change to 404 K and 98 kPa. (a) Estimate the change in the specific volume (Δv) of the gas using the ideal-gas relation and using Taylor's theorem. (b) Determine the exact answer
Estimate the specific-heat difference (cp - cv) for liquid water at 20 MPa and 60oC.
Estimate the specific-heat difference (cp - cv) for liquid water at 1000 psia and 150oF.
Plot the Joule-Thomson coefficient (μJ) for nitrogen over the pressure range of 100 psia to 1500 psia at the enthalpy values of 100 Btu/lbm, 175 Btu/lbm and 225 Btu/lbm. Discuss the results.
Determine the enthalpy change (Δh) and the entropy change (Δs) of nitrogen per unit mole as it undergoes a change of state from 225 K and 6 MPa to 320 K and 12 MPa, (a) By assuming ideal-gas behavior (b) By accounting for the deviation from ideal-gas behavior through the use of generalized charts
Determine the enthalpy change (Δh) and the entropy change (Δs) of carbon dioxide per unit mass as it undergoes a change of state from 250 K and 7 MPa to 280 K and 12 MPa, By assuming ideal-gas behavior By accounting for the deviation from ideal-gas behavior.
Derive the relation for the slope of the n = constant lines on a T-p diagram for a gas that obeys the van der Waals equation of state.
Methane is compressed adiabatically by a steady-state flow compressor from 2 MPa and -10oC to 10 MPa and 110oC at a rate of 0.8 kg/s. Using the generalized charts, determine the required power input to the compressor.
Methane gas flows through a pipeline with a mass flow rate of 110 lb/s at a pressure of 183 atm and a temperature of 56oF. Determine the volumetric flow rate (), in ft3/s, using (a) The ideal gas equation (b) Van der Waals equation (c) Compressibility chart.
Determine the specific volume (v) of water vapor at 10 MPa and 360oC, in m3/kg, using (a) The steam tables (b) Compressibility chart (c) Ideal gas equation.
Consider refrigerant R-12 vapor at 160oF and 0.5 ft3/lb. Estimate the pressure (p) at this state, in atm, using (a) The ideal gas equation (b) Van der Waals equation (c) Compressibility chart.
For the functions x = x(y, w), y = y(z, w), z = z(x, w), demonstrate that (∂x/∂y)w (∂y/∂z)w (∂z/∂x)w = 1.
The following expressions for the equation of state and the specific heat (cp) are obeyed by a certain gas: v = RT/paT2 and cp = ABTCp where a, A, B, C are constants. Obtain an expression for (a) the Joule-Thomson coefficient (μJ) and (b) the specific heat (cv).
The differential of pressure obtained from a certain equation of state is given by the following expression: dp = {2(v - b) / RT}dv - {(v - b)2 / RT2}dT. Determine the equation of state.
The differential of pressure obtained from a certain equation of state is given by the following expression: dp = {- RT/(v - b)2}dv + {R/(v - b)}dT. Determine the equation of state.
Derive the relation cp = - T(∂2g/∂T2)p
Prove that (∂β / ∂p)T = - (∂kT / ∂T)p.
Derive the relation for the volume expansivity (β) and the isothermal compressibility (kT) for (a) An ideal gas (b) A gas whose equation of state is p(v - b) = RT.
At certain states, the p-v-T data for a particular gas can be represented as Z = 1 - Ap/T4, where Z is the compressibility factor and A is a constant. Obtain an expression for the difference in specific heats (cp - cv).
Estimate the volume expansivity (β) and the isothermal compressibility (kT) of refrigerant-134a at 200 kPa and 30oC.

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