devarshi-dt-logo

Question:

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400K, 800K and 600K respectively. Choose the correct statement: The change in internal energy in the process AB is ΔR. The change in internal energy in the process BC is ΔR. The change in internal energy in the process CA is 700R. The change in internal energy in whole cyclic process is 250R.

The change in internal energy in the process CA is700R.

The change in internal energy in the process BC is�R.

The change in internal energy in the process AB is�R.

The change in internal energy in whole cyclin process is250R.

Solution:

For a diatomic gas, Cv = (5/2)R
ΔUAB = nCV(TB - TA) = 1 × (5R/2)(800 - 400) = 1000R
ΔUAC = ΔQAC - WAC = nCP(TA - TC) - nR(TA - TC) = nCV(TA - TC) = 1 × (5R/2)(400 - 600) = -500R
Thus, adding up the change in internal energy in both these processes, we get change in internal energy from C to B as 500R.
As the change in internal energy is a point function we get
ΔUBC = -500R