Gaseous hydrogen contained initially under standard conditions in sealed vessel of volume `V = 5 L` was cooled by `Delta T = 55 K`. Find how much the internal energy of the gas will change and what amount of heat will be lost by the gas.

Explanation

By the first law of thermodynamics,
`Q = Delta U + A`
Here `A = 0`, as the volume remains constant,
So, `Q = Delta U = (v R)/(gamma - 1) Delta T`
From gas law, `p_0 V = v R T_0`
So, `Delta U = (p_0 V Delta T)/(T_0(gamma - 1)) = -0.25 k J`
Hence amount of heat lost `= - Delta U = 0.25 k J`.