GATE 2026 MT – Question 54
2 moles of an ideal gas is reversibly expanded from 10 liter to 20 liter at isothermal condition. The value of universal gas constant R is 8.314 J/mol-K. If the temperature of the gas is 27 °C, the magnitude of work done in the process (rounded off to two decimal places) is ______________ Joules.
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Correct answer: 3440.00 to 3492.00
Explanation
For reversible isothermal expansion of an ideal gas, the work magnitude is $|W|=nRT\ln(V_f/V_i)$. Using the usual exam conversion $T=27+273=300\ \mathrm K$ and $V_f/V_i=20/10=2$ gives $|W|=2(8.314)(300)\ln2=$ **3457.70 J**.
Work done on the gas has the opposite sign. Using 273.15 in the temperature conversion gives about 3459.43 J; the retained official grading follows the stated exam convention.