Question
For an ideal gas, a process is described by P = kT, where k is a constant. If the molar heat capacity for this process is C, then which one of the following is correct (where the symbols have their usual meanings)?
NDA
General Ability
General Science
2026
NDA 2026 (Phase 1)
NDA General Ability Question (2026) — Solution
Options
- A. C = C_P
- B. C = C_V
- C. C = (C_P + C_V)/2
- D. C is never constant
Answer
B. C = C_V
Step-by-step solution
The ideal gas equation for n moles is PV = nRT. Given the process equation P = kT, where k is a constant. Substituting P into the ideal gas equation, we get: (kT)V = nRT V = nR k Since n, R, and k are constants, the volume V is constant. Thus, the process is isochoric. For an isochoric process, the work done dW = P dV = 0. From the first law of thermodynamics, dQ = dU + dW = dU. Since dU = nC_V dT and dQ = nC dT, we have: nC dT = nC_V dT C = C_V Answer: C = C_V
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