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Calculate the total work done when one mole of a gas expands isothermally from an initial volume of 20dm³ to a final volume of 40dm³ at 298 K given R = 8.314 J / K mol

Calculate the total work done when one mole of a gas expands isothermally from an initial volume of 20dm³ to a final volume of 40dm³ at 298 K given R = 8.314 J / K mol

Grade:11

2 Answers

Shailendra Kumar Sharma
188 Points
6 years ago
Work done is isothermal process is nRTln(V2/V1) = 1*8.314*298{ln(40/20)}
so the work done is 1717.32 Jole the work done in volume increase will be +ve
Aditya Prabhu
26 Points
2 years ago
As this is isothermal reversible process, we use the formula:

W= -2.303 nRT log \frac{V2}{V1} …........ (1)
 
Given,
R= 8.314 J/K/mol
V1= 20 dm3 = 2000 L
V2= 40 dm3 = 4000L
T= 298 K
 
Substitute these values in equation (1)
W= -2.303 × 8.314 × 298 log2               (log2 = 0.3010)
W= -1717.46 J
 
As the volume is expanding , W cannot be negative.
\therefore W= 1717.46 J

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