Physical Chemistry Third Edition

2.2 Heat 51

2.6 a.Obtain a formula for the work done in reversibly and
isothermally compressing 1.000 mol of a gas from a
volumeV 1 to a volumeV 2 if the gas obeys the
Redlich–Kwong equation of state.
b.Using the formula from part a, find the work done in
reversibly compressing 1.000 mol of carbon dioxide
from 10.00 L to 5.000 L at 298.15 K. Compare with the
result obtained by assuming that the gas is ideal.
c.Using the formula from part a, calculate the work done
on the surroundings if 1.000 mol of carbon dioxide
expands isothermally but irreversibly from 5.000 L to
10.00 L at an external pressure of 1.000 atm. Compare
with the result obtained by assuming that the gas is ideal.

2.7 a.Obtain a formula for the work done in reversibly and
isothermally compressing 1.000 mol of a van der Waals
gas from a volumeV 1 to a volumeV 2.
b.Using the formula from part a, find the work done in
reversibly compressing 1.000 mol of carbon dioxide

from 10.00 L to 5.000 L at 298.15 K. Compare with the

result obtained by assuming that the gas is ideal.

c.Using the formula from part a, calculate the work done

on the surroundings if 1.000 mol of carbon dioxide

expands isothermally but irreversibly from 5.000 L to

10.00 L at an external pressure of 1.000 atm. Compare

with the result obtained by assuming that the gas is ideal.

2.8Test the following differentials for exactness:

a.T^2 dT+TVdV

b.xexydx+yexydy

c.xydx+^12 x^2 dy

2.9Carry out the line integral:

∫

c

(

nR

V

dT−

nRT

V^2

dV

)

on the path from (300.0 K, 10.0 L) to (300.0 K, 20.0 L) to

(400.0 K, 20.0 L). Taken 1 .000 mol.

2.2 Heat

Joseph Black was the first to distinguish between the quantity of heat and the

“intensity” of heat (temperature) and to recognizelatent heatabsorbed or given

off in phase transitions. However, Black believed in thecaloric theory of heat,

which incorrectly asserted that heat was an “imponderable” fluid called “caloric.”

This incorrect theory was not fully discredited until several decades after Black’s

death.

Joseph Black, 1728–1799, was a
Scottish chemist who discovered
carbon dioxide (“fixed air”) by heating
calcium carbonate.

Heat Transferred during Temperature Changes

A small amount of heat added to a system is proportional to its change in temperature

of the system if there is no phase change or chemical reaction:

dqCdT (2.2-1)

wheredqis an infinitesimal amount of heat transferred to the object anddTis a resulting

infinitesimal change in temperature. The proportionality constantCis called theheat

capacityof the system.

Equation (2.2-1) doesnotindicate thatCis a derivative ofqwith respect toT.We

will see thatdqis an inexact differential so that the heat capacityCdepends on the way

in which the temperature of the system is changed. If the temperature is changed at

constant pressure, the heat capacity is denoted byCPand is called theheat capacity at

constant pressure. If the temperature is changed at constant volume, the heat capacity

is denoted byCVand is called theheat capacity at constant volume. These two heat

capacities are not generally equal to each other.