2.2 Work and Heat
2.1.Calculate the work performed by a person who exerts a
force of 30 N (N newtons) to move a box 30 meters if the
force were (a)exactly parallel to the direction of movement,
and (b)45° to the direction of movement. Do the relative
magnitudes make sense?
2.2.Explain in your own words why work done by the sys-
tem is defined as the negativeof pV, not positive pV.
2.3.Calculate the work in joules when a piston moves re-
versibly from a volume of 50. mL to a volume of 450. mL
against a pressure of 2.33 atm.
2.4.Calculate the work in joules needed to expand a balloon
from 5 mL to 3.350 L against standard atmospheric pressure.
(Your lungs provide that work if you are blowing it up your-
self.) Assume a reversible process.
2.5.Consider exercise 2.4. Would the work be more or less if
it were performed against different external pressures found
(a)at the top of Mount Everest, (b)at the bottom of Death
Valley, (c)in space? (d)What if the process were performed
irreversibly?
2.6.Calculate the heat capacity of a material if 288 J of en-
ergy were required to heat 50.5 g of the material from 298 K
to 330 K. What are the units?
2.7.Liquid hydrogen fluoride, liquid water, and liquid am-
monia all have relatively high specific heats for such small mol-
ecules. Speculate as to why this might be so.
2.8.A 7.50-g piece of iron at 100.0°C is dropped into 25.0 g
of water at 22.0°C. Assuming that the heat lost by the iron
equals the heat gained by the water, determine the final tem-
perature of the iron/water system. Assume a heat capacity of
water of 4.18 J/gK and of iron, 0.45 J/gK.
2.9.With reference to Joule’s apparatus in Figure 2.6, assum-
ing a mass of 100. kg of water (about 100 L), a weight with
a mass of 20.0 kg, and a drop of 2.00 meters, calculate how
many drops it would take to raise the temperature of the wa-
ter by 1.00°C. The acceleration due to gravity is 9.81 m/s^2.
(Hint:see Example 2.5.)
2.10.Some people have argued that rocket engines will not
work because the gaseous products of a rocket engine, push-
ing against the vacuum of space, do not perform any work,
and therefore the engine will not propel anything. Refute this
argument. (Hint:consider Newton’s third law of motion.)
2.11.Verify equation 2.8.
2.3 Internal Energy; First Law
of Thermodynamics
2.12.The statement “Energy can be neither created nor de-
stroyed” is sometimes used as an equivalent statement of the
first law of thermodynamics. There are inaccuracies to the
statement, however. Restate it to make it less inaccurate.
2.13.Explain why equation 2.10 is not considered a contra-
diction of equation 2.11.
2.14.What is the change in internal energy when a gas con-
tracts from 377 mL to 119 mL under a pressure of 1550 torr,
while at the same time being cooled by removing 124.0 J of
heat energy?
2.15.Calculate the work for the isothermal, reversible com-
pression of 0.245 mole of an ideal gas going from 1.000 L to
1 mL if the temperature were 95.0°C.
2.16.Calculate the work done when 1.000 mole of an ideal
gas expands reversibly from 1.0 L to 10 L at 298.0 K. Then,
calculate the amount of work done when the gas expands ir-
reversibly against a constant external pressure of 1.00 atm.
Compare the two values and comment.
2.17.Suppose a change in a gaseous system is adiabatic and
isothermal. What do you think the change in internal energy
would be for such a change?2.4 & 2.5 State Functions; Enthalpy
2.18.The distance between downtown San Francisco and
downtown Oakland is 9 miles. However, a car driving between
the two points travels 12.3 miles. Of these distances, which
one is analogous to a state function? Why?
2.19.Is temperature a state function? Defend your answer.
2.20.A piston reversibly and adiabatically contracts 3.88
moles of ideal gas to one-tenth of its original volume, then ex-
pands back to the original conditions. It does this a total of
five times. If the initial and final temperature of the gas is
27.5°C, calculate (a)the total work and (b)the total Ufor
the overall process.
2.21.Many compressed gases come in large, heavy metal
cylinders that are so heavy that they need a special cart to
move them around. An 80.0-L tank of nitrogen gas pressur-
ized to 172 atm is left in the sun and heats from its normal
temperature of 20.0°C to 140.0°C. Determine (a)the final
pressure inside the tank and (b)the work, heat, and Uof the
process. Assume that behavior is ideal and the heat capacity
of diatomic nitrogen is 21.0 J/molK.
2.22.Under what conditions will Ube exactly zero for a
process whose initial conditions are not the same as its final
conditions?
2.23.A balloon filled with 0.505 mole of gas contracts re-
versibly from 1.0 L to 0.10 L at a constant temperature of
5.0°C. In doing so, it loses 1270 J of heat. Calculate w, q, U,
and Hfor the process.
2.24.It takes 2260 J to vaporize a gram of liquid water to
steam at its normal boiling point of 100°C. What is Hfor this
process? What is the work, given that the water vapor expands
against a pressure of 0.988 atm? What is Ufor this process?2.6 Changes in State Functions
2.25.If the infinitesimals of internal energy were taken with
respect to pressure and volume, what would be the equation
for the infinitesimal change in internal energy dU? Write a sim-
ilar expression for dH, assuming the same variables.Exercises for Chapter 2 63EXERCISES FOR CHAPTER 2