A 0.510-mol sample of an ideal diatomic gas at 392 kPa and 330 K expands quasi-s

Question

A 0.510-mol sample of an ideal diatomic gas at 392 kPa and 330 K expands quasi-statically until the pressure decreases to 158 kPa. Find the final temperature and volume of the gas, the work done by the gas, and the heat absorbed by the gas if the expansion is the following.

(b) adiabatic

final temperature     
? K
volume of the gas     
? L
work done by the gas     
? J
heat absorbed     
? J

Please complete the answers. As I have to post this question on the second time, as the last person only answer part a

Thanks!

Explanation / Answer

V1 = nRT/P1

V1 = 0.510*8.314*330 / 392*1000 = 3.5695*10-3 m3

Now for an adiabatic process:

P1V11.4 =  P2V21.4

so,

392k*(3.5695*10-3)1.4 = 158k*V21.4

V2 = 6.83*10-3 m3

1) Final temperature, T2 = P2V2/nR = 158k*6.83*10-3/[0.51*8.314] = 254.54 K

2) Volume of the gas, V2 = 6.83*10-3 m3

W = [T1 - T2][V21-1.4 - V11-1.4]/[1-1.4] = [330-254.54][{6.83*10-3}1-1.4 - {3.5695*10-3 }1-1.4]/[-0.4]

3) Work done by the gas, W = 410.87 J

4) Heat absorbed, Q = 0;

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