CBSE · Class 11 · Physics · ThermodynamicsThe adiabatic bulk modulus of elasticity ($Ea$) of an ideal gas at pressure $P$ is equal to:
Step-by-Step Solution
For an adiabatic process, $PV^\gamma = \text{constant}$. Differentiating gives $\Delta P \cdot V^\gamma + P \gamma V^{\gamma-1} \Delta V = 0 \implies -V \frac{\Delta P}{\Delta V} = \gamma P$. Thus, adiabatic bulk modulus $E_a = \gamma P$.
Detailed Options Breakdown
Option : $P$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Thermodynamics.
Option 1: $\gamma P$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: $\frac{P}{\gamma}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Thermodynamics.
Option 3: $\gamma^2 P$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Thermodynamics.
💡 Study Guide: This question tests core syllabus concepts from Thermodynamics. For formulas, key summaries, and mock exam reference guides, read the full Thermodynamics Revision Notes.