Question

Consider a closed system of one mole of an ideal gas undergoing a polytropic process. The process follows \( PV^n = \text{constant} \), where P is the pressure, V is the volume and n is a constant. If the process is isobaric, which one of the following is the value of n?

• A. 0
• B. 1
• C. \( \infty \)
• D. the ratio of specific heat capacity at constant pressure to specific heat capacity at constant volume

Hint:

Set the exponent on volume to zero so pressure alone remains constant in PV^n = C.

Answer 1

The Correct Option is A

Start from PV^n = C. Take n = 0: the equation becomes PV^0 = P = C, so pressure alone is pinned constant while volume is free to change - exactly "isobaric." Next take n = 1: PV = C. For fixed gas, PV = RT (per mole), so PV = C forces T to be constant too - isothermal, not isobaric. As n grows without bound, V tends to a constant regardless of P - isochoric. Finally, n = gamma corresponds to the isentropic process. Since the question asks specifically for the isobaric case, only n = 0 fits. \[ \boxed{n = 0} \]