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Question
3 mole of a gas at temperature 400 K expands isothermally from an initial volume of 4 litres to a final volume of 8 litres. Find the work done by the gas. (R = 8.31 J mol-1 K-1)
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Solution
Given:
n = 3 mol, T = 400 K, Vi = 4 L, Vf = 8 L, R = 8.31 J mol-1 K-1
To find: Work done by gas (W)
Formula: `"W"_"isothermal"` = nRT In`"V"_"f"/"V"_"i"`
Calculation:
From formula (i),
W = 3 × 8.31 × 400 × In`(8/4)`
Now, ln x = 2.303 × log (x)
∴ In`(8/4)` = ln (2) = 2.303 log (2)
∴ W = 1200 × 8.31 × 2.303 × 0.3010
= antilog{log(1200) + log(8.31) + log (2.303) + log(0.3010)}
= antilog{3.0792 + 0.9196 + 0.3623 + (`overline1`.4786 )}
= antilog{3.8397}
= 6.913 × 103 J
= 6.913 kJ
Work done by the gas is 6.913 kJ.
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