Problem 2

One mole of monatomic ideal gas initially at absolute temperature

T_i

and pressure

p

is heated slowly at constant pressure to

T_f>T_i

. It obeys

pV=R_gT

, where

R_g

is the gas constant; neglect macroscopic kinetic and potential energy changes. Take work done by the gas and heat entering it as positive. (a) Find the volume change and work done by the gas. (b) Find the change in internal energy. (c) Find the heat added and the ratio of heat to work.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

W=\int_{V_i}^{V_f}p\,dV=p\Delta V=R_g\Delta T

problems.proof.analysis

Work done by the gas is $\int p\,dV$ . Constant pressure reduces this to $p\Delta V$ , which the state relation expresses through temperature.