Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermodpnmics 17

where p is the ambient gas pressure and p is the corresponding gas density.

Obtain expressions for

(a) The speed of sound in a gas for which the compressions and rar-

efactions are isothermal.

(b) The speed of sound in a gas for which the compressions and rar-

efactions are adiabatic.

( Wisconsin)

Solution:
The isothermal process of an ideal gas follows pV = const; the adiabatic
process of an ideal gas follows pV7 = const. We shall use pVt = const for
a general process, its differential equation being

dp dV

-+t-=O.

PV

Thus

(2) = -tv P.

With p = M/V, we have

RT

Therefore

(a) The isothermal process: t = 1, thus c = dm.

(b) The adiabatic process: t = 7, thus c = dm.

1021

Two systems with heat capacities C1 and Cz, respectively, interact

thermally and come to a common temperature Tf. If the initial temperature

of system 1 was TI, what was the initial temperature of system 2? You may

assume that the total energy of the combined systems remains constant.

( wis co nsin)