Question

One mole of an ideal gas at atmospheric pressure expands isobarically from a volume of 1m³ to a volume of 2m³.

1 - Find the initial and final temperatures of the gas

2 - Find the work done by the gas

3 - Find the heat added to the gas

Answer 1

(a) For 1 mole of ideal gas the equation of state is

PV = RT

Where, R = 8.314 J/mol.K and we will use

1 atm = 1.01*105 Pa

In initial state, PiVi = RTi

Or, 1.01*105*1 = 8.314*Ti

So, initial temperature, Ti = (1.01*105/8.314) K

= 12148 K

For isobaric system, we can write,

Vi/Vf = Ti/Tf

Or, Tf = (Vf/Vi)*Ti

= {(2*12148)/1} K

Thus, final temperature, Tf = 24296 K

(b) Work done, W = P(Vf - Vi)

= {1.01*105*(2-1)} J

= 1.01*105 J

(c) Heat added, Q = Cp(Tf - Ti)

Where, Cp = specific heat at constant pressure

= 5R/2 = (5*8.314/2) J/mol.K

= 20.785 J/mol.K

So, heat = {20.785*(24296-12148)} J

= 252496.18 J