An ideal gas is expanding such that PT³ = constant. The coefficient of volume expansion of the gas is :

Solution

Physics sir · 4 steps

Swap P for nRT/V first, and the process turns into a simple power law between V and T.

1. Remove the pressure. For an ideal gas, P = nRT/V. Put this into PT³ = constant to get nRT⁴/V = constant.
2. Volume versus temperature. Since n and R are fixed, V = cT⁴, where c is a constant. The volume grows as the fourth power of temperature.
3. Apply the definition. The coefficient of volume expansion is 1/VdV/dT. Differentiate V = cT⁴ to get dV/dT = 4cT³.

   1/VdV/dT = 4cT³/cT⁴ = 4/T

4. So. The coefficient of volume expansion is 4/T, which is option (c).

The idea to keep. For any process, use the gas law to get V as a power of T. If V ∝ Tᵏ, the coefficient of volume expansion is k/T.

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