Physics Principles with Applications 7th edition Douglas C. Giancoli - Solutions

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An ideal gas goes through a polytropic process with exponent n. Find the mean free path k and the number of collisions of each molecule per second λ as a function of. (a) The volume V; (b) The pressure p; (c) The temperature T.
Determine the molar heat capacity of a polytropic process through which an ideal gas consisting of rigid diatomic molecules goes and in which the number of collisions between the molecules remains constant (a) In a unit volume; (b) In the total volume of the gas.
An ideal gas of molar mass M is enclosed in a vessel of volume V whose thin walls are kept at a constant temperature T. At a moment t = 0 a small hole of area S is opened, and the gas starts escaping into vacuum. Find the gas concentration n as a function of time t if at the initial moment n (0) =
A vessel filled with gas is divided into two equal parts I and 2 by a thin heat-insulating partition with two holes. One hole has a small diameter, and the other has a very large diameter (in comparison with the mean free path of molecules). In part 2 the gas is kept at a temperature η times
As a result of a certain process the viscosity coefficient of an ideal gas increases a = 2.0 times and its diffusion coefficient β = 4.0 times. How does the gas pressure change and how many times?
How will a diffusion coefficient D and the viscosity coefficient η of an ideal gas change if its volume increases n times? (a) Isothermally; (b) Isobarically?
An ideal gas consists of rigid diatomic molecules. How will a diffusion coefficient D and viscosity coefficient η change and how many times if the gas volume is decreased adiabatically n = l0 times?
An ideal gas goes through a polytropic process. Find the polytropic exponent n if in this process the coefficient (a) Of diffusion; (b) Of viscosity; (c) Of heat conductivity remains constant.
Knowing the viscosity coefficient of helium under standard conditions, calculate the effective diameter of the helium atom.
The heat conductivity of helium is 8.7 times that of argon (under standard conditions). Find the ratio of effective diameters of argon and helium atoms.
Under standard conditions helium fills up the space between two long coaxial cylinders. The mean radius of the cylinders is equal to R, the gap between them is equal to AT/, with T/
A gas fills up the space between two long coaxial cylinders of radii R1 and R2, with R1 < R2. The outer cylinder rotates with a fairly low angular velocity co about the stationary inner cylinder. The moment of friction forces acting on a unit length of the inner cylinder is equal to N 1. Find the
Two identical parallel discs have a common axis and are located at a distance h from each other. The radius of each disc is equal to a, with a >> h. One disc is rotated with a low angular velocity co relative to the other, stationary, disc. Find the moment of friction forces acting on the
Solve the foregoing problem, assuming that the discs are located in an ultra-rarefied gas of molar mass M, at temperature T and under pressure p.
Making use of Poiseuille's equation (1.7d), find the mass μ of gas flowing per unit time through the pipe of length I and radius a if constant pressures Pl and p2 are maintained at its ends.
One end of a rod, enclosed in a thermally insulating sheath, is kept at a temperature T1 while the other, at T2. The rod is composed of two sections whose lengths are l1 and l2 and heat conductivity coefficients ×1 and ×2. Find the temperature of the interface
Two rods whose lengths are l1 and l2 and heat conductivity coefficients ×1 and ×2 are placed end to end. Find the heat conductivity coefficient of a uniform rod of length l1 + l2 whose conductivity is the same as that of the system of these two rods. The lateral surfaces of the rods are assumed
A rod of length l with thermally insulated lateral surface consists of material whose heat conductivity coefficient varies with temperature as × = a/T, where a is a constant. The ends of the rod are kept at temperatures T1 and T2. Find the function T (x), where x is the distance from the end whose
Two chunks of metal with heat capacities C1 and C2 are interconnected by a rod of length l and cross-sectional area S and fairly low heat conductivity ×. The whole system is thermally insulated from the environment. At a moment t = 0 the temperature difference between the two chunks of metal
Find the temperature distribution in a substance placed between two parallel plates kept at temperatures T1 and T2. The plate separation is equal to l, the heat conductivity coefficient of the substance × ∞V T.
The space between two large horizontal plates is filled with helium. The plate separation equals l = 50 mm. The lower plate is kept at a temperature T1 = 290 K, the upper, at = 330 K. Find the heat flow density if the gas pressure is close to standard.
The space between two large parallel plates separated by a distance l = 5.0 mm is filled with helium under a pressure p = t.0 Pa. One plate is kept at a temperature tl = 17 °C and the other, at a temperature t2 = 37 °C. Find the mean free path of helium atoms and the heat flow density.
Find the temperature distribution in the space between two coaxial cylinders of radii R1 and R2 filled with a uniform heat conducting substance if the temperatures o[ the cylinders are constant and are equal to T1 and T 2 respectively.
Solve the foregoing problem for the case of two concentric spheres of radii R1 and R2 and temperatures T1 and T2.
A constant electric current flows along a uniform wire with cross-sectional radius R and heat conductivity coefficient ×. A unit volume of the wire generates a thermal power w. Find the temperature distribution across the wire provided the steady-state temperature at the wire surface is equal to T
The thermal power of density w is generated uniformly inside a uniform sphere of radius R and heat conductivity coefficient ×. Find the temperature distribution in the sphere provided the steady-state temperature at its surface is equal to To
A saturated water vapour is contained in a cylindrical vessel under a weightless piston at a temperature t = 100 °C. As a result of a slow introduction of the piston a small fraction of the vapour Δm = 0.70 g gets condensed. What amount of work was performed over the gas? The vapour is
A vessel of volume V = 6.0 1 contains water together with its saturated vapour under a pressure of 40 arm and at a temperature of 250 °C. The specific volume of the vapour is equal to Vv = 50 1/kg under these conditions. The total mass of the system water-vapour equals m = 5.0 kg. Find the mass
The saturated water vapour is enclosed in a cylinder under a piston and occupies a volume Vo = 5.0 1 at the temperature t = 100 °C. Find the mass of the liquid phase formed after the volume under the piston decreased isothermally to V = 1.6 1. The saturated vapour is assumed to be ideal.
A volume occupied by a saturated vapour is reduced isothermally n-fold. Find what fraction η of the final volume is occupied by the liquid phase if the specific volumes of the saturated vapour and the liquid phase differ by N times (N > n). Solve the same problem under the condition that the
An amount of water of mass m = 1.00 kg, boiling at standard atmospheric pressure, turns completely into saturated vapour. Assuming the saturated vapour to be an ideal gas find the increment of entropy and internal energy of the system.
Water of mass m = 20 g is enclosed in a thermally insulated cylinder at the temperature of 0 °C under a weightless piston whose area is S = 410 cm2 . The outside pressure is equal to standard atmospheric pressure. To what height will the piston rise when the water absorbs Q = 20.0 kJ of heat?
One gram of saturated water vapour is enclosed in a thermally insulated cylinder under a weightless piston. The outside pressure being standard, m = 1.0 g of water is introduced into the cylinder at a temperature to = 22 °C. Neglecting the heat capacity of the cylinder and the friction of the
If an additional pressure Δp of a saturated vapour over a convex spherical surface of a liquid is considerably less than the vapour pressure over a plane surface, then Δp = (pv/pl) 2a/r, where pv and pl are the densities of the vapour and the liquid, a is. the surface tension, and r is
Find the mass .of all molecules leaving one square centimetre of water surface per second into a saturated water vapour above it at a temperature t = 100 °C. It is assumed that η = 3.6% of all water vapour molecules falling on the water surface are retained in the liquid phase.
Find the pressure of saturated tungsten vapour at a temperature T = 2000 K if a tungsten filament is known to lose a mass μ = 1.2.10-13 g/(s . cm 2) from a unit area per unit time when evaporating into high vacuum at this temperature.
By what magnitude would the pressure exerted by water on the walls of the vessel have increased if the intermolecular attraction forces had vanished?
Find the internal pressure p1 of a liquid if its density p and specific latent heat of vaporization q are known. The heat q is assumed to be equal to the work performed against the forces of the internal pressure, and the liquid obeys the Van der Waals equation. Calculate p1 in water.
Demonstrate that Eqs. (2.6a) and (2.6b) are valid for a substance, obeying the Van der Waals equation, in critical state. Instruction makes use of the fact that the critical state corresponds to the point of inflection in the isothermal curve p (V).
Calculate the Van der Waals constants for carbon dioxide if its critical temperature Ter, = 304 K and critical pressure per = 73 atm.
Find the specific volume of benzene (C6H6) in critical state if its critical temperature Ter = 562 K and critical pressure Per = 47 atm.
Write the Van der Waals equation via the reduced parameters , , and T, having taken the corresponding critical values for the units of pressure, volume, and temperature. Using the equation obtained, find how many times the gas temperature exceeds its critical temperature if the gas pressure is t2
Knowing the Van der Waals constants, find: (a) The maximum volume which water of mass m = 1.00 kg can occupy in liquid state; (b) The maximum pressure of the saturated water vapour.
Calculate the temperature and density of carbon dioxide in critical state, assuming the gas to be a Van der Waals one.
What fraction of the volume of s vessel must liquid ether occupy at room temperature in order to pass into critical state when temperature is reached? Ether has Tcr = 467 K, per = 35.5 atm, M = 74 g/mol.
Demonstrate that the straight line 1-5 corresponding to the isothermal-isobaric phase transition cuts the Van der Waals isotherm so that areas I and II are equal (Fig. 2.5).
What fraction of water super cooled down to the temperature t = – 20°C under standard pressure turns into ice when the system passes into the equilibrium state? At what temperature of the super cooled water does it turn into ice completely?
Find the increment of the ice melting temperature in the vicinity of 0 °C when the pressure is increased by Δp = 1.00 atm. The specific volume of ice exceeds that of water by ΔV ' = 0.091 cm3/g.
Find the specific volume of saturated water vapour under standard pressure if a decrease of pressure by Δp = 3.2 kPa is known to decrease the water boiling temperature by ΔT = 0.9 K.
Assuming the saturated water vapour to be ideal, find its pressure at the temperature t0t.t °C.
A small amount of water and its saturated vapour are en- closed in a vessel at a temperature t = 100 °C. How much (in per cent) will the mass of the saturated vapour increase if the temperature of the system goes up by ΔT = 1.5 K? Assume that the vapour is an ideal gas and the specific volume
Find the pressure of saturated vapour as a function of temperature p (T) if at a temperature To its pressure equals pe. Assume that: the specific latent heat of vaporization q is independent of T, the specific volume of liquid is negligible as compared to that of vapour saturated vapour obeys the
An ice which was initially under standard conditions was compressed up to the pressure p = 640 atm. Assuming the lowering of the ice melting temperature to be a linear function of pressure under the given conditions, find what fraction of the ice melted. The specific volume of water is less than
In the vicinity of the triple point the saturated vapour pressure p of carbon dioxide depends on temperature T as log p = a = 1 – b/T, where a and b are constants. If p is expressed in atmospheres, then for the sublimation process a = 9.05 and b = 1.80 kK, and for the vaporization process a =
Water of mass m = 1.00 kg is heated from the temperature t1, = 10 °C up to t1 = 100°C at which it evaporates completely. Find the entropy increment of the system.
The ice with the initial temperature t1 = 0 °C was first melted, then heated to the temperature t1 = 100 °C and evaporated. Find the increment of the system's specific entropy.
A piece of copper of mass m = 90 g at a temperature t1 = 90 °C was placed in a calorimeter in which ice of mass 50 g was at a temperature – 3 °C. Find the entropy increment of the piece of copper by the moment the thermal equilibrium is reached.
A chunk of ice of mass ml = 100 g at a temperature tx = 0 °C was placed in a calorimeter in which water of mass m1 = 100 g was at a temperature t1. Assuming the heat capacity of the calorimeter to be negligible, find the entropy increment of the system by the moment the thermal equilibrium is
Molten lead of mass m = 5.0 g at a temperature t2 = 327 °C (the melting temperature of lead) was poured into a calorimeter packed with a large amount of ice at a temperature t1 = 0 °C. Find the entropy increment of the system lead-ice by the moment the thermal equilibrium is reached. The specific
A water vapour filling the space under the piston of a cylinder, is compressed (or expanded) so that it remains saturated all the time, being just on the verge of condensation. Find the molar heat capacity C of the vapour in this process as a function of temperature T, assuming the vapour to be an
One mole of water being in equilibrium with a negligible amount of its saturated vapour at a temperature T1 was completely converted into saturated vapour at a temperature T2. Find the entropy increment of the system. The vapour is assumed to be an ideal gas the specific volume of the liquid is
What happens to the work done when a jar of orange juice is vigorously shaken?
When a hot object warms a cooler object, does temperature flow between them? Are the temperature changes of the two objects equal?
(a) If two objects of different temperatures are placed in contact, will heat naturally flow from the object with higher internal energy to the object with lower internal energy?(b) Is it possible for heat to flow even if the internal energies of the two objects are the same? Explain
In warm regions where tropical plants grow but the temperature may drop below freezing a few times in the winter, the destruction of sensitive plants due to freezing can be reduced by watering them in the evening. Explain.
The specific heat of water is quite large. Explain why this fact makes water particularly good for heating systems (that is, hot-water radiators).
Why does water in a metal canteen stay cooler if the cloth jacket surrounding the canteen is kept moist?
Explain why burns caused by steam on the skin are often more severe than burns caused by water at 100oC?
Explain why water cools (its temperature drops) when it evaporates, using the concepts of latent heat and internal energy.
Will potatoes cook faster if the water is boiling faster?
Does an ordinary electric fan cool the air? Why or why not? If not, why use it?
Very high in the Earth’s atmosphere, the temperature can be 700oC, Yet an animal there would freeze to death rather than roast. Explain.
Explorers on failed Arctic expeditions have survived by covering themselves with snow. Why would they do that?
Why is wet sand at the beach cooler to walk on than dry sand?
If you hear that an object has “high heat content” does that mean that its temperature is high? Explain.
When hot-air fumaces are used to heat a house, why is it important that there be a vent for air to return to the fumace? What happens if this vent is blocked by a bookcase?
Ceiling fans are sometimes reversible, so that they drive the air down in one season and pull it up in another season. Which way should you set the fan for summer for winter?
Down sleeping bags and parkas are often specified as so many inches or centimeters of loft, the actual thickness of the garment when it is fluffed up. Explain.
Microprocessor chips have a “heat sink” glued on top that looks like a series of fins. Why is it shaped like that?
Sea breezes are often encountered on sunny days at the shore of a large body of water. Explain in light of the fact that the temperature of the land rises more rapidly than that of the nearby water.
The floor of a house on a foundation under which the air can flow is often cooler than floor that rests directly on the ground (such as a concrete slab foundation). Explain.
A 22oC day is warm, while a swimming pool at 22oC feels cool. Why?
Explain why air temperature readings are always taken with the thermometer in the shade.
A premature baby in an incubator can be dangerously cooled even when the air temperature in the incubator is warm. Explain.
Why the liner of a thermos bottle is silvered (Fig 14-15). And why does it have a vacuum between its two walls?
Imagine you have a wall that is very well insulated-it has a very high thermal resistance, R1. Now you place a window in the wall that has a relatively low R-value, R2. What has happened to the overall R-value of the wall plus window, compared to R1 and R2?
Heat loss occurs through windows by the following processes; (1) ventilation around edges; (2) through the frame, particularly if it is metal; (3) through the glass panes; and (4) radiation.(a) For the first three, what is (are) the mechanism (s); conduction, convection, or radiation?(b) Heavy
A piece of wood lying in the Sun absorbs more heat than a piece of shiny metal. Yet the wood feels less hot than the metal when you pick it up. Explain.
The Earth cools off at night much more quickly when the weather is clear than when cloudy. Why?
An “emergency blanket” is a thin shiny (metal coated) plastic foil. Explain how it can help to keep an immobile person warm.
Explain why cities situated by the ocean tend to have less extreme temperatures than inland cities at the same latitude.
How much heat (in joules) is required to raise the temperature of 30.0 kg of water from 15oC to 95oC?
To what temperature will 7700 J of heat raise 3.0 kg of water that is initially at 10.0oC?
An average active person consumes above 2500 Cal a day.(a) What is this in joules?(b) What is this is kilowatt-hours?(c) Your power company charges about a dime per kilowatt-hour. How much would your energy cost per day if you bought it from the power company could you feed yourself on this much
A British thermal unit (Btu) is a unit of heat in the British system of units. One Btu is defined as the heat needed to raise 1. IB of water by 1Fo show that 1 Btu = 0.252 kcal = 1055 J.
A water heater can generate 32,000 kJ/h how much water can it heat from 15oC to 50oC per hour?
A small immersion heater is rated at 350 W. Estimate how long it will take to heat a cup of soup (assume this is 250mL of water) from 20oC to 60oC.
How many kilocalories are generated when the brakes are used to bring a 1200-kg car to rest from a speed of 95 km/h?
An automobile cooling system holds 16 L of water. How much heat does it absorb if its temperature rises from 20oC to 90oC?
What is the specific heat of a metal substance if 135 kJ of heat is needed to raise 5.1 kg of the metal from 18.0oC to 31.5oC?

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Physics Principles with Applications 7th edition Douglas C. Giancoli - Solutions

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