Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 3.4-5

SOME FORMAL RELATIONSHIPS, AND SAMPLE SYSTEMS

Physics — Statistical Mechanics · ideal-gas-polytropic-process

Problem

In a particular engine a gas is compressed in the initial stroke of the piston. Measurements of the instantaneous temperature, carried out during the compression, reveal that the temperature increases according to

T = \left(\frac{V}{V_0}\right)^\eta T_0

where

T_0

and

V_0

are the initial temperature and volume, and

\eta

is a constant. The gas is compressed to the volume

V_1

(where

V_1 < V_0

). Assume the gas to be monatomic ideal, and assume the process to be quasi-static.

a

) Calculate the work

W

done on the gas.

b

) Calculate the change in energy

\Delta U

of the gas.

c

) Calculate the heat transfer

Q

to the gas (through the cylinder walls) by using the results of

(a)

and

(b)

d

) Calculate the heat transfer directly by integrating

dQ = T\,dS

e

) From the result of

(c)

(d)

, for what value of

\eta

Q = 0

? Show that for this value of

\eta

the locus traversed coincides with an adiabat (as calculated in Problem 3.4-2).

Related theory

Ideal Gas Equation And Absolute Temperature

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