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mechanical engineering

Thermodynamics An Interactive Approach 1st edition Subrata Bhattacharjee - Solutions

Two different fuels are being considered for a 1 MW (net output) heat engine which can operate between the highest temperature produced during the burning of the fuel and the atmospheric temperature of 300 K. Fuel A burns at 2500 K, delivering 50 MJ/kg (heating value) and costs $2 per kilogram.
The specific enthalpy (h) of an ideal gas is a function of temperature (T) only as can be seen from Table D-3 for air.(a) Using the data from the table, determine the specific heat at constant pressure (cp) of air at 400 K.(b) What-if Scenario: What would cp be if the temperature were 800 K?
Use the PC system state daemon to evaluate (a) cp. (b) cv of steam at 100 kPa and 150oC. Use a 1oC difference between the neighboring states. What-if Scenario: What would the (c) cp (d) cv be if the pressure were 300 kPa?
The cp of a working substance is known to be 2.0 kJ/kg-K at 500 K. A software is used to simulate the heating of the substance at constant pressure (cp). It produces the following behavior: At 500 K, it produces an enthalpy (h) of 2000 kJ/kg, while at 501 K, it produces a value of 2005 kJ/kg. Do
The temperature of a gas is related to its absolute pressure and specific volume through T = 3.488pv, where T, p, and v are expressed in their standard SI units. Consider a gas at 100 kPa and 1 m3/kg. (a) Estimate the change in temperature (ΔT) using Taylor's theorem if the state of the gas
The temperature of a gas is related to its absolute pressure and specific volume through T = 3.488pv, where T, p and v are expressed in their standard SI units. Consider a gas at 350 K and 1 m3/kg. (a) Estimate the change in pressure (Δp) using Taylor's theorem if the state of the gas changes to
The second T-ds relation reduces to Tds = dh at constant pressure (cp), use the superheated table of water (Table B-3) to evaluate the two sides of this equation at (a) 100 kPa, 200oC. (b) 50 MPa, 500oC. Calculate for dT = 10oC. (c) What-if Scenario: What would the answer in part (b) be if the PC
The first T-ds relation reduces to Tds = pdv if the internal energy remains constant. Use the PC system state daemon to evaluate the state of steam at 100 kPa and 200oC. Also evaluate two neighboring states at 99 kPa and 101 kPa, holding internal energy constant and compare the two sides of the
Using the PC state daemon, calculate from first principle (a) cp (b) cv of steam at 100 kPa and 320oC. Use a 1oC difference in setting up the neighboring states. (c) What is the ratio of (cp - cv)/R for steam at this state? (d) What-if Scenario: What would be the answer in part (c) if the steam is
Determine the changes in (a) Specific enthalpy (Δh). (b) Specific entropy (Δs) if the pressure of liquid water is increased from 100 kPa to 1 MPa at a constant temperature of 25oC. Use the SL model for water.
A block of iron of volume 1 m3 undergoes the following change of state. State-1: p1 = 100 kPa, T1 = 20oC, V1 = 0, z1 = 0; State-2: p2 = 500 kPa, T2 = 30oC, V2 = 30 m/s, z2 = 100 m. Determine (a) ΔE. (b) ΔU. (c) ΔH. (d) ΔS.
A thermal storage is made of a granite rock bed of 10 m3 which is heated to 425 K using solar energy. A heat engine receives heat from the bed and rejects the waste heat to the ambient surroundings at 290 K. During the process, the rock bed cools down and as it reaches 290 K, the engine stops
A copper block of mass 5 kg, initially at equilibrium with the surroundings at 30oC and 100 kPa, is placed in a pressurized chamber with a pressure of 20 MPa and a temperature of 200oC. Determine (a) The change in the internal energy (ΔU). (b) Enthalpy (ΔH) (c) Entropy (ΔS) of the block after it
A 20 kg block of aluminum at 97.4oC is dropped into a tank containing 10 kg of water at 1oC. If the final temperature after equilibrium is 30oC, determine (a) ΔU. (b) ΔS for the combined system of aluminum and water after the process is complete.
A 20-kg block of iron (specific heat 0.45 kJ/kg-K) is heated by conduction at a rate of 1 kW. Assuming the block to be uniform at all time, determine the rate of change of temperature (dT/dt).
A copper bullet of mass 0.1 kg, traveling at 400 m/s, hits a copper block of mass 2 kg at rest and becomes embedded. The combined system moves with a velocity of 19.05 m/s in accordance with the conservation of momentum principle. Both the bullet and copper block are at 25oC initially. Assuming the
A cup of coffee cools down by transferring heat to the surroundings at a rate of 1 kW. If the mass of the coffee is 0.2 kg and coffee can be modeled as water, determine the rate of change of temperature (dT/dt) of coffee.
A pump raises the pressure of liquid water from 50 kPa to 5000 kPa in an isentropic manner. Determine (a) The change in temperature (ΔT). (b) Specific enthalpy (Δh) between the inlet and exit.
Water flows through an adiabatic pumping system at a steady flow rate (m) of 5 kg/s. The conditions at the inlet are p1 = 90 kPa, T1 = 15oC and z1 = 0 m; and the conditions at the exit are p2 = 500 kPa, T2 = 17oC and z2 = 200 m. (a) Simplify the energy equation to derive an expression for the
Oil (cv = 1.8 kJ/kg-K, ρ = 910 kg/m3) flows steadily through a long insulated constant-diameter pipe at a volume flow rate of 10 m3/min. The conditions at the inlet are p = 3000 kPa, T = 20oC, V = 20 m/s and z = 100 m. The conditions at the exit are p = 2000 kPa and z = 0 m. (a) Evaluate the
A cup of coffee of volume 0.3 L is heated from a temperature of 25oC to 60oC at a pressure of 100 kPa. Determine the change in the (a) Internal energy (ΔU). (b) Enthalpy (ΔH). (c) Entropy (ΔS). Assume the density (ρ) and specific heat of coffee to be 1100 kg/m3 and 4.1 kJ/kg-K respectively.
Water flows steadily through a device at a flow rate of 20 kg/s. At the inlet, the conditions are 200 kPa and 10oC. At the exit, the conditions are 2000 kPa and 50oC. (a) Determine the difference between the entropy (S) transported by the flow at the exit and at the inlet. (b) What are the possible
In an isentropic nozzle, operating at steady state, the specific flow energy (j) and specific entropy (s) remain constant along the flow. The following properties are known at the inlet and exit ports of an isentropic nozzle discharging water at a steady rate of 2 kg/s. Inlet: p1 = 300 kPa, A1 = 4
For copper, plot how the internal energy (U), and entropy (S), vary with T within the range 25oC - 1000oC. Use the SL system state daemon.
For liquid water, plot how the internal energy (U), and entropy (S), vary with T within the range 25oC - 100oC. Use the SL system state daemon.
A block of solid with a mass of 10 kg is heated from 25oC to 200oC. If the change in the specific internal energy (Δu) is found to be 67.55 kJ/kg, identify the material (aluminum: 1; copper: 2; iron: 3; wood: 4; sand: 5).
A system contains an unknown solid of unknown mass, which is heated from 300 K to 900 K at 100 kPa. The change in internal energy (ΔU) of the system is measured as 61.02 MJ. Using the SL model, determine the change in entropy (ΔS) of the system.
A block of aluminum with a mass of 10 kg is heated from 25oC to 200oC. Determine (a) The total change in internal energy (ΔU). (b) Entropy (ΔS) of the block. (c) What-if Scenario: What would the change in entropy be if the block were made of copper instead?
A 2 kg block of aluminum at 600oC is dropped into a cooling tank. If the final temperature (T2) at equilibrium is 25oC, determine (a) The change in internal energy (ΔU) . (b) The change in entropy (ΔS) of the block as the system. Use the SL model for aluminum (cv = 0.902 kJ/kg-K).
A 3 kg block of iron at 800oC is dropped into 50 kg of water in an insulated cooling tank. If the final temperature (T2) at equilibrium is 29.9oC, determine (a) The change in internal energy (ΔU). (b) The change in entropy (ΔS) of the block and water as the system. Use the SL model for iron (cv =
The heat transfer necessary to raise the temperature of a constant-volume closed system is given by Q = ΔU. Using the SL model, compare the heat necessary to raise the temperature by 10oC for such a system of 1 kg and composed of (a) Liquid water. (b) Liquid ethanol. (c) Crude oil.
Repeat the above problem (3-2-8 [TF]) for the following solids as the working substance: (a) Gold. (b) Iron. (c) Sand. (d) Granite.
A cylinder contains H2O (and nothing else). The outside temperature is 298 K. To analytically determine the pressure inside, you figure that the temperature of H2O must be also 298 K. Also, you shake the cylinder and realize that it is only partially filled with liquid water. You say, "Aha",
Determine the boiling temperature of water (a) At sea level and (b) Atop Mount Everest (elevation 8,848 m). Use Table H-3 to look up the pressure of atmosphere at different altitudes.
A vertical piston-cylinder assembly contains water. The piston has a mass of 2 kg and a diameter of 10 cm. Determine the vertical force necessary on the piston to ensure that water inside the cylinder boils at (a) 120oC. (b) 80oC. Assume atmospheric pressure to be 101 kPa. (c) What-if Scenario:
A vertical piston-cylinder assembly contains a saturated mixture of water at 120oC and a gauge pressure of 108.5 kPa. The piston has a mass of 5 kg and a diameter of 12 cm. Determine(a) The atmospheric pressure outside.(b) The external force exerted on the piston to maintain a constant pressure.
A cooking pan with an inner diameter of 20 cm is filled with water and covered with a lid of mass 5 kg. If the atmospheric pressure is 100 kPa, determine (a) The boiling temperature of water. (b) What-if Scenario: What would the boiling temperature be if a 5 kg block were placed on top of the lid?
A heat engine cycle is executed with ammonia in the saturation dome. The pressure of ammonia is 1.5 MPa during heat addition and 0.6 MPa during heat rejection. What is the highest possible thermal efficiency? Based on the temperatures of heat addition and rejection, could you comment on possible
Plot how the saturation temperature of water increases with pressure. Use the full range from the triple point to critical point.
Plot the phase diagram (p-T) for the following refrigerants for a temperature range from 40oC to the critical temperature:(a) R-134a.(b) R-12.(c) NH3. Use a log scale for pressure and linear scale for temperature.
Complete the following property table for H2O. Also locate the states on a T-s diagram (qualitatively).
Complete the following property table for Refrigerant-134a. Also locate the states on a T-s diagram (qualitatively).
A 10 L rigid tank contains 0.01 kg of steam. Determine (a) The pressure (p). (b) Stored energy (E). (c) Entropy (S), of steam if the quality is 50%. Neglect kinetic and potential energy. What-if Scenario: What would the (d) Pressure. (e) Stored energy. (f) Entropy of steam be if the steam quality
Saturated liquid water flows through a pipe at 10 MPa. Assuming thermodynamic equilibrium to exist at any given cross-section. (a) Determine the temperature (T). (b) The quality of water. A small leak develops and as water jets out, it quickly equilibrates with the pressure outside, which is at 100
A liquid-vapor mixture of water at 100 kPa has a quality of 1%. (a) Determine the volumetric quality of the mixture. (b) What-if Scenario: What would the volumetric quality be if the working fluid were R-134a?
A 0.4 m3 vessel contains 10 kg of refrigerant-134a at 25oC. Determine the (a) Phase composition (b) Pressure (p) (c) Total internal energy (U). (d) Total entropy (S) of the refrigerant.
A tank contains 1 L of saturated liquid and 99 L of saturated vapor of water at 200 kPa. Determine (a) The mass. (b) Quality. (c) Stored energy (E) of the steam.
A tank contains 20 kg of water at 85oC. If half of it (by mass) is in the liquid phase and the rest in vapor phase, determine (a) The volumetric quality, the stored energy (E) in (b) The liquid. (c) Vapor phases.
A vessel having a volume of 0.5 m3 contains a 2 kg saturated mixture of H2O at 500 kPa. Calculate the (a) Mass of liquid (b) Mass of vapor. (c) Volume of liquid (d) Volume of vapor.
(a) What is the phase composition of H2O at p = 100 kPa and u = 1500 kJ/kg?(b) How much volume does 2 kg of H2O in that state occupy?(c) What-if Scenario: What would the volume be if mass of H2O were 5 kg?
A rigid vessel contains 3 kg of refrigerant-12 at 890 kPa and 85oC. Determine (a) Volume of the vessel (b) Total internal energy (U).
For H2O, plot how the volume fraction, y, changes with quality, x, over the entire possible range at (a) p = 100 kPa (b) p = 20 MPa.
A rigid tank of volume 83 m3 contains 100 kg of H2O at 100oC. The tank is heated until the temperature inside reaches 120oC. Determine the pressure (p) inside the tank at (a) The beginning. (b) The end of the heating process. (c) What-if Scenario: What would the final pressure be if the tank
A tank contains 5 kg of saturated liquid and 5 kg of saturated vapor of H2O at 500 kPa. Determine (a) Its volume in m3 an (b) Its temperature (T) in Celcius. The tank is now heated to a temperature of 250oC. (c) Determine the pressure in MPa.
A 30-cm diameter pipe carries H2O at a rate of 10 kg/s. At a certain cross-section, steam is found to be saturated vapor at 200oC. Determine (a) The pressure (kPa). (b) Velocity (m/s).
A tank contains 500 kg of saturated liquid and 5 kg of saturated vapor of H2O at 500 kPa. Determine (a) The quality of the steam. (b) The volume of the tank.
Determine the change in(a) Stored energy (ΔE).(b) Entropy (ΔS) of the system.(c) Using the entropy balance equation, explain why the entropy of the system increases.For Information: Problem 3-3-29 [FK],
A tank with a volume of 10 gallons contains a liquid-vapor mixture of propane at 30oC. Determine (a) The pressure. (b) The mass of propane inside. (c) If the tank is designed for a maximum pressure of 3000 kPa, determine the maximum temperature the tank will be able to withstand.
A piston cylinder device of volume 1 m3 contains 3 kg of water. The piston, which has an area of 100 cm2, exerts a force of 1.7 kN on the pin to keep it stationary. Determine (a) The temperature. (b) Quality of H2O inside the cylinder. The water is now heated. (c) Determine the force on the pin
A rigid tank with a volume of 3.5 m3 contains 5 kg of saturated liquid-vapor mixture of H2O at 80oC. The tank is slowly heated until all the liquid in the tank is completely vaporized. Determine the temperature at which this process occurred. Also show the process on a T-v diagram with respect to
A 10 m3 rigid tank contains saturated vapor of H2O at 200oC. The tank is cooled until the quality drops to 80%. Determine the (a) Mass of H2O in the tank. (b) Drop in pressure (Δp). (c) Drop in temperature (ΔT). (d) Drop in total entropy (ΔS). (e) What causes the entropy of this system to
A 1000 L rigid tank contains saturated liquid water at 40oC. (a) Determine the pressure (p) inside. The tank is now heated to 90oC. (b) Use the compressed liquid table to determine the pressure in the tank.
A lid with negligible weight is suddenly placed on a pan of boiling water and the heating is turned off. After about an hour, thermal equilibrium is reached between the water and the atmosphere, which is at 30oC and 101 kPa. If the inner diameter of the pan is 20 cm, determine (a) The force
Superheated water vapor at 1.5 MPa and 280oC is allowed to cool at constant volume until the temperature drops to 130oC. At the final state, determine (a) The pressure (p2). (b) The quality. (c) The specific enthalpy (h2). Show the process on a T-s diagram.
A rigid tank contains steam at the critical state. Determine (a) The quality of the steam after the tank cools down to the atmospheric temperature, 25oC. (b) What percent of the volume is occupied by the vapor at the final state?
For H2O, locate (qualitatively) the following states on a T-s and a p-v diagram. State- 1: p = 100 kPa, T = 50oC; State-2: p = 5 kPa, T = 50oC; State-3: p = 500 kPa, x = 50%.
A rigid tank with a volume of 1 m3 contains superheated steam at 500 kPa and 500oC. Determine(a) The mass.(b) Total internal energy (U) of the steam. The tank is now cooled until the total internal energy decreases to 2076.2 kJ. Determine(c) The pressure (p2).(d) Temperature (T2) in the final state.
10 kg of ammonia is stored in a rigid tank of volume 0.64 m3. Determine the pressure variation (Δp) in the tank as the ambient temperature swings between(a) 5oC in the night to(b) 40oC in the day time.(c and d) What-if Scenario: What would the answers be if the volume of the tank were increased to
A large industrial tank of volume 200 m3 is filled with steam at 450oC and 150 kPa. Determine (a) The pressure (p). (b) Quality of steam when the temperature drops to 25oC due to heat loss. (c) If the heat transfer for this constant volume process is given by Q = ΔU, determine the heat transfer.
A rigid tank of volume 0.64 m3 contains 10 kg of water at 5oC. (a) Plot how the state of water changes in a T-s diagram as the temperature is gradually increased to 500oC. (b) What-if Scenario: How would the plot change if the tank held 0.1 kg of water?
Draw a line of constant specific volume that passes through the critical point on a Ts diagram for R-134a. (b) What-if Scenario: How would the line shift if it passed through saturated vapor state at 50oC?
A 1 m3 rigid tank contains 2.3 kg of a vapor-liquid mixture of water. The tank is heated to raise the quality of steam. Plot how the pressure and temperature in the tank vary as the quality of steam gradually increases to 100%.
Plot how(a) The pressure (p).(b) The stored energy (E).(c) The entropy (S) of 4.5 kg of water contained in a 2 m3 rigid vessel as the temperature is increased from 30oC to 300oC.
A piston-cylinder device contains 3 kg of saturated mixture of water with a quality of 0.8 at 180oC. Heat is added until all the liquid vaporizes. Determine (a) The pressure (p). (b) The initial volume. (c) The final volume. (d) The work (W) performed by the vapor during the expansion process.
A piston-cylinder device initially contains 3 ft3 of liquid water at 60 psia and 63oF. Heat is now transferred to the water at constant pressure until the entire liquid is vaporized. Determine (a) The mass of the water. (b) Final temperature (T2). (c) Total enthalpy change (ΔH). The T-s diagram is
A piston-cylinder device contains 0.6 kg of steam at 350oC and 1.5 MPa. Steam is now cooled at constant pressure until half of the mass condenses. Determine(a) The final temperature (T2).(b) The boundary work transfer.(c) Show the process on a T-s diagram.
For H2O, locate (qualitatively) the following states on a T-s and a p-v diagram. State- 1: p = 10 kPa, saturated liquid; State-2: p = 1 MPa, s = s1; State-3: p = p2, T = 500oC State-4: p = p1, saturated vapor.
Water vapor (1 kg) at 0.2 kPa and 30oC is cooled in a constant pressure process until condensation begins. Determine (a) The boundary work transfer. (b) Change of enthalpy (ΔH) treating water as the system. What-if Scenario: What would the (c) Boundary work transfer (d) Change of enthalpy be if
A piston cylinder device contains 10 L of liquid water at 100 kPa and 30oC. Heat is transferred at constant pressure until the temperature increases to 200oC. Determine the change in (a) The total volume. (b) Total internal energy (ΔU) of steam. Show the process on a T-s and p-v diagram.
A piston-cylinder device contains a saturated mixture of water with a quality of 84.3% at 10 kPa. If the pressure is raised in an isentropic (constant entropy) manner to 5000 kPa, (a) Determine the final temperature (T2). (b) What-if Scenario: What would the final temperature be if water were at
A piston-cylinder device contains a saturated mixture of R-134a with a quality of 90% at 50 kPa. The quality of the mixture is raised to 100% by (i) compressing the mixture in an isentropic manner or, alternatively, (ii) by adding heat in a constant temperature process. (a) Draw the two processes
Draw the constant pressure line on a T-s diagram for H2O at p = 100 kPa as liquid water is heated to superheated vapor. Redo the plot for a pressure of 500 kPa.
For H2O, plot how the entropy (S) changes with T in the superheated vapor region for a pressure of (a) 10 kPa. (b) 100 kPa. (c) 10 MPa. Take at least 10 points from the saturation temperature to 800oC.
Water at a pressure of 50 MPa is heated in a constant pressure electrical heater from 50oC to 1000oC. Spot the states on a T-s diagram and determine (a) The change of specific enthalpy (Δh). (b) Specific entropy (Δs). Use compressed liquid model for liquid water.
Determine: (a) The mass flow rate. (b) The volume flow rate of steam flowing through a pipe of diameter 0.1 m at 1000 kPa, 300oC and 50 m/s. (c) Also determine the rate of transport of energy by the steam. (d) What-if Scenario: What would the answer in (c) be if the temperature were 400oC?
Refrigerant-134a flows through a pipe of diameter 5 cm with a mass flow rate of 0.13 kg/s at 100 kPa and 10 m/s. Determine(a) The temperature (T).(b) Quality of the refrigerant in the pipe. Also determine the rate of transport of(c) Energy (J).(d) Entropy (S) by the flow.
Steam at a pressure of 2 MPa and 400oC flows through a pipe of diameter 10 cm with a velocity of 50 m/s. Determine the flow rates of (a) Mass (m). (b) Energy (J). (c) Entropy (S).
A sealed rigid tank contains saturated steam at 100 kPa. As the tank cools down to the temperature of the surrounding atmosphere, the quality of the steam drops to 5%. Using a T- s diagram, explain why the pressure in the tank must decrease drastically to satisfy thermodynamic equilibrium.
Liquid water at 100 kPa, 30oC enters a boiler through a 2 cm-diameter pipe with a mass flow rate of 1 kg/s. It leaves the boiler as saturated vapor through a 20 cm-diameter pipe without any significant pressure loss. Determine (a) The exit velocity (V2), the rate of transport of energy at (b) The
Repeat the above problem (3-3-60 [DV]) for a boiler pressure of 1 MPa. Problem (3-3-60) Liquid water at 100 kPa, 30oC enters a boiler through a 2 cm-diameter pipe with a mass flow rate of 1 kg/s. It leaves the boiler as saturated vapor through a 20 cm-diameter pipe without any significant pressure
Water is pumped in an isentropic (constant entropy) manner from 100 kPa, 25oC to 40 MPa. Determine the change in specific enthalpy (Δh) usingThe compressed liquid table.
Water at 30 MPa and 20oC is heated at constant pressure until the temperature reaches 300oC. Determine (a) The change in specific volume (Δv). (b) Specific enthalpy (Δh). Use compressed liquid table for water. (c) What-if Scenario: What would the specific enthalpy be if water were only heated to
Draw a constant pressure line (p = 100 kPa) on a T-v and a T-s diagram for H2O. Repeat the problem with p = 1000 kPa.
In an isentropic nozzle the specific flow energy (j) and entropy (s) remain constant along the flow. Superheated steam flows steadily through an isentropic nozzle for which the following properties are known at the inlet and exit ports. Inlet: p = 200 kPa, T = 400oC, A = 100 cm2, V = 5 m/s; Exit: p
Steam enters a turbine, operating at steady state, at 5000 kPa and 500oC with a mass flow rate of 5 kg/s. It expands in an isentropic manner to an exit pressure of 10 kPa. Determine (a) The exit temperature (T2). (b) Exit quality and the volumetric flow rate at (c) The inlet. (d) Exit.
Refrigerant-134a enters a throttle valve as saturated liquid at 40oC and exits at 294 kPa. If enthalpy remains constant during the flow, determine (a) The drop in pressure (Δp). (b) The drop in temperature (ΔT) in the valve.
Saturated vapor of R-134a enters a compressor, operating at steady state at 160 kPa with a volume flow rate of 10 L/min. The specific entropy remains constant along the flow. Determine (a) The exit temperature (T2) if the compressor raises the pressure of the flow by a factor of 10. Also, determine
Repeat the above problem (3-3-68 [DJ]) with refrigerant-12 as the working fluid. Problem (3-3-68) Saturated vapor of R-134a enters a compressor, operating at steady state at 160 kPa with a volume flow rate of 10 L/min. The specific entropy remains constant along the flow. Determine (a) The exit
An isentropic compressor is used to raise the pressure of a refrigerant, entering the compressor as saturated vapor. Using a T-s diagram, explain why the temperature at the exit can be expected to be higher than that at the inlet.
Water flows steadily through a 10 cm-diameter pipe with a mass flow rate of 1 kg/s. The flow enters the pipe at 200 kPa, 30oC and is gradually heated until it leaves the pipe at 300oC without any significant drop in pressure. Plot the flow velocity against the temperature of the flow.

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