An ideal gas initially at 0° C temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is 3 / 2, the change in temperature due to the thermodynamic process is _________ K.

Solution

Physics sir · 3 steps

Sudden compression means no time for heat to flow, so treat it as adiabatic and use TV^(γ-1).

1. Adiabatic process. A sudden compression leaves no time for heat exchange, so the process is adiabatic. For an adiabatic change, TV^(γ-1) stays constant.

   T₂ = T₁(V₁/V₂)^(γ-1)

2. Put in numbers. Convert first: T₁ = 0°C = 273 K. With V₁/V₂ = 4 and γ - 1 = 1/2, you get T₂ = 273 × 4^(1/2) = 273 × 2 = 546 K.
3. So. The change in temperature is 546 - 273 = 273 K.

The common slip: 546. Stopping at the final temperature gives 546, but the question asks for the change, 546 - 273 = 273 K.

The idea to keep. Sudden means adiabatic. Use TV^(γ-1) = constant, always in kelvin, and read carefully whether the question asks for the final temperature or the change.

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