A diatomic gas is enclosed in a vessel fitted with massless movable piston. Area of cross section of vessel is `1m^2`. Initial height of the piston is 1m (see the figure). The initial temperature of the gas is 300K. The temperature of the gas is increased to 400K, keeping pressure constant, calculate the new height of the piston. The piston is brought to its initial position with no heat exchange. Calculate the final temperature of the gas. You can leave answer in fraction.

Answer

`400((4)/(3))^(0.4) K`

Explanation

At constant pressure
`V alpha T implies (V_(2))/(V_(1)) = (T_(2))/(T_(1)) implies (Ah_(2))/(Ah_(1)) = (T_(1))/(T_(1))`
`therefore h_(2) = h_(1) ((T_(2))/(T_(1))) = (1.0) ((400)/(300))m = (4)/(3)m`
As there is no heat loss , process is adiabatic.
For adiabatic process
`T_(f)V_(f)^(gamma-1) = T_(t)V_(t)^(gamma-1)`
`therefore T_(f) = T_(t)((V_(t))/(V_(f)))^(gamma-1) = (400)((h_(t))/(h_(f)))^(1.4-1) = 400((4)/(3))^(0.4)`