Two moles of an ideal gas at 300 K were cooled at constant volume so that the pressure is reduced to half the initial value. Then as a result of heating at constant pressure, the gas expands till it attains the original temperature. Find the total heat absorbed by the gas, if R is the gas is constant : 

300R J

For 1 mol of gas : \(\Delta Q = C_V \Delta T + P\Delta T\)

At constant volume : \(\Delta T = 0\)

For 2 moles of gas : \(\Delta Q = 2C_V \Delta T\)

From : PV = nRT = 2R x 300 and 

\(\frac{P}{2}V = 2RT_f\)

\(\Rightarrow T_f = 150 \) K

\(\Rightarrow \Delta Q = 2C_V (T_f - T_i)\)

\(\Rightarrow \Delta Q = 2C_V (150-300)\) = -300 C_V J

In the next process : \(\Delta Q = 2C_P \Delta T = 2C_P (300 - 150)\0

\(\Delta Q = 300 C_P \) J

Net heat absorbed = - 300 C_V + 300 C_P = 300 (C_P - C_V)

  = 300R J