A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be :

Solution

Physics sir · 3 steps

Sudden compression at constant entropy means adiabatic, so use PV^γ = constant with γ = 5/3.

1. Identify the process. A sudden compression leaves no time for heat to flow, and constant entropy says the same thing. The process is reversible adiabatic, so PV^γ stays constant.
2. Value of gamma. A monoatomic gas has C_V = 3/2R and C_P = 5/2R, so γ = C_P/C_V = 5/3.

   P₂ = P(V/(V/8))^(5/3) = P × 8^(5/3) = P × (2³)^(5/3) = 2⁵P

3. So. The final pressure is 32P, which is option (c).

The idea to keep. Sudden or insulated means adiabatic: PV^γ is constant, not PV. Write the volume ratio as a power of 2 and the fractional power of γ becomes easy.

Answer from the NTA final answer key. Solution by PrepWiser.