A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of 800 cm³ and temperature 27° C. The change in temperature when the gas is adiabatically compressed to 200 cm³ is:
(Take γ=1.5 ; γ is the ratio of specific heats at constant pressure and at constant volume)

Solution

Physics sir · 3 steps

Insulated walls mean adiabatic, so use TV^(γ-1) constant, with the temperature in kelvin.

1. Adiabatic relation. No heat can cross the walls, so the compression is adiabatic. For an adiabatic process TV^(γ-1) stays constant, and T must be in kelvin: T₁ = 27 + 273 = 300 K.

   T₂ = T₁(V₁/V₂)^(γ-1)

2. Put in numbers. V₁/V₂ = 800/200 = 4 and γ - 1 = 0.5. So T₂ = 300 × 4^(0.5) = 300 × 2 = 600 K.
3. So. The change in temperature is T₂ - T₁ = 600 - 300 = 300 K, which is option (a).

The idea to keep. Thermally insulated walls mean an adiabatic process. Use TV^(γ-1) = constant, always in kelvin, and read whether the question asks for the final value or the change.

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