question_answer

During adiabatic changes, the volume of a gas is found to depend inversely on the square of its absolute temperature. Find how its pressure will depend on the absolute temperature.

Answer:

                Given \[V\propto \frac{1}{{{T}^{2}}}\] or            \[\text{V = }\frac{\text{constant}}{{{\text{T}}^{\text{2}}}}\] But     \[\frac{PV}{T}=\] constant \[\therefore \]  \[\frac{\text{P}}{\text{T}}\text{.}\frac{\text{constant}}{{{\text{T}}^{\text{2}}}}\text{=}\] constant or \[P\propto {{T}^{3}}\]