Question
An ideal gas of bulk modulus K is enclosed in a container of fixed walls. Find the stress set up in the gas when heated through temperature θ. Let γ be the temperature coefficient of cubical expansion of gas.
Solution
Given, an ideal gas of bulk modulus 'K' and is heated to a temperature .
Increase of temperature of gas at constant volume is equivalent if the gas is first heated at constant pressure and then compressed isothermally to original volume.
Let V be the volume of gas. When it is heated through a temperature θ at constant pressure, then the increase in volume of gas is,
∆V = Vγθ
Now compress the gas isothermally so that the volume decreases by ∆V = Vγθ.
If ∆P be the stress set up in the gas, then
