A monoatomic ideal gas undergoes a process in which the work done by the gas equals Q/4, where Q is the heat absorbed. Find the molar heat capacity of the gas during this process in terms of the gas constant R.

5R/2
7R/2
3R/2
2R

Correct answer: 2R

Solution

From the first law: Delta U = Q - W = Q - Q/4 = 3Q/4. For a monoatomic ideal gas, Delta U = n*(3R/2)*Delta T. So n*Delta T = (3Q/4) / (3R/2) = Q/(2R). Since Q = n*C*Delta T, we get C = Q / (n*Delta T) = Q / (Q/2R) = 2R.

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