Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V₂ = 2V₁ then the ratio of temperature T₂/T₁ is :

Solution

Physics sir · 3 steps

Swap P for nRT/V in the curve's equation and you get a direct rule linking T and V.

1. Use the gas law. For one mole of ideal gas, P = RT/V. Put this into the process equation PV^(1/2) = constant.

   RT/V V^(1/2) = constant ⇒ T/√V = constant ⇒ T ∝ √V

2. Put in numbers. T₂/T₁ = √(V₂/V₁) = √(2V₁/V₁) = √2.
3. So. The temperature rises by a factor of √2, which is option (a).

The idea to keep. For any process PVⁿ = constant, substitute P = nRT/V to get TVⁿ⁻¹ = constant. Then any temperature ratio follows from the volume ratio.

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