Problems and Solutions on Thermodynamics and Statistical Mechanics

32 Problem, E/ Solutiom on Thermodynumica d Statistical Mechanica

(a) What is the final temperature Tf?

(b) What is the work delivered?

(GUSPEA)

(a) The internal energy is U = NCT. Thus dQ1 = NCdT1 and dQ2 =

Solution :

dQi dQ2

Tl T2

NCdT2. For a Carnot engine, we have - = --. Hence

Tf dT1 Tf dT2 In-=-ln-, Tr Tf

Thus Li = K’ Tl T2

Therefore Tf = m.

(b) Conservation of energy gives

w = (Ul - U) - (U - U2) = u, + u2 - 2u

= NC(Ti+ T2 - 2Tf).

1036

Water powered machine. A self-contained machine only inputs two

equal steady streams of hot and cold water at temperatures TI and T2. Its

only output is a single high-speed jet of water. The heat capacity per unit

mass of water, C, may be assumed to be independent of temperature. The

machine is in a steady state and the kinetic energy in the incoming streams

is negligible.

(a) What is the speed of the jet in terms of T1,TZ and T, where T is

(b) What is the maximum possible speed of the jet?

the temperature of water in the jet?

Fig. 1.13.