The pressure (P) and temperature (T) relationship of an ideal gas obeys the equation PT²= constant. The volume expansion coefficient of the gas will be :

Solution

Physics sir · 3 steps

Use PV = nRT to swap P for V, so you get V in terms of T, then differentiate.

1. Remove P. From the ideal gas equation, P = nRT/V. Put this into PT² = constant to get nRT³/V = constant.
2. Volume law. Here n and R are fixed, so V ∝ T³. Write it as V = kT³, where k is a constant.

   γ = 1/VdV/dT = 3kT²/kT³ = 3/T

3. So. The volume expansion coefficient is 3/T, which is option (d).

The idea to keep. Whenever a gas follows an unusual P–T or P–V law, first use PV = nRT to turn it into V ∝ Tᵐ. Then the volume expansion coefficient is m/T.

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