Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 7.4-11

STABILITY OF THERMODYNAMIC SYSTEMS

Physics — Statistical Mechanics · adiabatic-compression-oxygen-final-pressure

Problem

Two moles of

\mathrm{O_2}

are initially at a pressure of

10^5

Pa and a temperature of

0^\circ

C. An adiabatic compression is carried out to a final temperature of

300^\circ

C. Find the final pressure by integration of equation 7.39. Assume that

\mathrm{O_2}

is a simple ideal gas with a molar heat capacity

c_p

which can be represented by

c_p = 26.20 + 11.49 \times 10^{-3}T - 3.223 \times 10^{-6}T^2

where

c_p

is in J/mole and

T

is in kelvins. Answer:

P_f \approx 15 \times 10^5 \text{ Pa}