A diatomic ideal gas is heated at constant at constant volume until the pressure is doubled and again heated of constant pressure until the volume is doubled. The average molar heat capacity for the whole process is

Options

A. `(13R)/(6)`
B. `(19R)/(6)`
C. `(23R)/(6)`
D. `(17R)/(6)`

Answer

B

Explanation

Let initial pressure, volume, temperature be `P_(0), V_(0), T_(0)` indicated by state A in P-V diagram. The gas is then isochorically taken to state `B(2P_(0), V_(0), 2T_(0))` and then taken from state B to state `C(2P_(0), 2V_(0), 4T_(0))` isobarically.

Total heat absorbed 1 mole of gas
`DeltaQ= C_(V)(2P_(0) -T_(0)) +C_(P) (4T_(0) -2T_(0))`
`=(5)/(2) RT_(0) +(7)/(2) R xx 2T_(0) =(19)/(2) RT_(0)`
Total change in temperature from state A to C is
`DeltaT=3T_(0)`
molar heat capacity `=(DeltaQ)/(DeltaT)= ((19)/(2)RT_(0))/(3T_(0)) = (19)/(6)R`.