One mole of an ideal monoatomic gas undergoes a process described by PV³ = constant. The heat capacity of the gas during this process is:
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One mole of an ideal monoatomic gas undergoes a process described by PV³ = constant. The heat capacity of the gas during this process is:

G1 Physics · Accepted Answer

Step 1: For a monoatomic ideal gas, molar Cᵥ = (3/2)R. Step 2: Given PV³ = constant. Taking logarithmic differentials: dP/P + 3dV/V = 0. Step 3: From PV = RT (one mole), R dT = P dV + V dP = P dV − 3P dV = −2P dV. Step 4: Thus P dV = −(R/2)dT. Step 5: First law gives δQ = dU + P dV = (3/2)R dT − (1/2)R dT = R dT. Step 6: Process heat capacity C = δQ/dT = R. Final answer: (D).