The piston cylinder arrangement shown contains a diatomic gas at temperature 400K. The cross-sectional area of the cylinder is `1m^2` . Initially the height of the piston above the base of the cylinder is The temperature is now raised to at constant pressure.

If the piston is now brought back to its original height without any heat loss, find the new equilibrium temperature of the gas (in K).

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)`