Problems and Solutions on Thermodynamics and Statistical Mechanics

14 Problem €4 Sdutiona on Thermcdpamica d stati8ticd Mechanic8

(d) How much heat is required if the volume is kept constant?
Take the specific heat at constant volume c, = 5 cal/mole "C and
R = 2 cal/mole.'C.
( Wisconsin)

Solution:
(a) We consider nitrogen to be an ideal gas. The heat required is

1000

28

Q = n(c, + R)AT = -(5 + 2) x 120 = 30 x 103cal

(b) The increase of the internal energy is

100

28

AU = nc,AT = - x 5 x 120

= 21 x 10~~~1.

(c) The external work done is

W = Q - AU = 8.6 x lo3 cal.

(d) If it is a process of constant volume, the required heat is

Q = nc,AT = 21 x 103cal.

1018
10 litres of gas at atmospheric pressure is compressed isothermally to
a volume of 1 litre and then allowed to expand adiabatically to 10 litres.
(a) Sketch the processes on a pVdiagram for a monatomic gas.
(b) Make a similar sketch for a diatomic gas.
(c) Is a net work done on or by the system?
(d) Is it greater or less for the diatomic gas?
( was co nsin)

Solution:
We are given that VA = lOl,V, = ll,Vc = 101 and pA = 1 atm..
A -+ B is an isothermal process, thus

pV = const. or ~AVA = ~BVB ,