Question

If \( \frac{C_p}{C_v} \) is unity for a process, \( PV^{\gamma} = \text{constant} \), then the process is:

• A. Adiabatic
• B. Isothermal
• C. Isobaric
• D. Isochoric

Hint:

For adiabatic processes, the relationship \( PV^{\gamma} = \text{constant} \) holds, where \( \gamma \) is the heat capacity ratio. This equation is specific to adiabatic compression or expansion in thermodynamics.

Answer 1

The Correct Option is A

The relation \( PV^{\gamma} = \text{constant} \) is the equation for an adiabatic process, where \( \gamma = \frac{C_p}{C_v} \) is the heat capacity ratio. - Adiabatic process refers to a process where no heat is exchanged with the surroundings, i.e., \( Q = 0 \). In this case, the process follows the equation \( PV^{\gamma} = \text{constant} \), where \( \gamma = \frac{C_p}{C_v} \). - Isothermal process is characterized by a constant temperature, and the equation for an isothermal process is \( PV = \text{constant} \), not \( PV^{\gamma} = \text{constant} \). - Isobaric process refers to a process occurring at constant pressure, and its equation is \( P = \text{constant} \), not \( PV^{\gamma} = \text{constant} \). - Isochoric process occurs at constant volume, and the equation is \( V = \text{constant} \), not \( PV^{\gamma} = \text{constant} \). Thus, \( PV^{\gamma} = \text{constant} \) corresponds to an adiabatic process.