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

Question

A diatomic ideal gas is heated at constant volume until the pressure is doubled and again heated at constant pressure until the volume is doubled. The average molar heat capacity for the whole process is (A) (1 3 R/6) (B) (1 9 R/6) (C) (2 3 R/6) (D) (1 7 R/6)

Tardigrade Admin · Accepted Answer

Let initial pressure, volume and temperature be

P_{0}, V_{0}

and

T_{0}

, respectively, indicated by state

A

in P-V diagram.
The gas is then isochorically taken to state

B (2 P_{0}, V_{0}, 2 T_{0})

and then taken from state

B

to state

C (2 P_{0}

,

2 V_{0}, 4 T_{0}

) isobarically.
Solution

Total heat absorbed by

1 m o l

of gas

Δ Q = C_{v} 2 T_{0} - T_{0} + C_{P} 4 T_{0} - 2 T_{0}

= \frac{5}{2} R T_{0} + \frac{7}{2} R \times 2 T_{0} = \frac{19}{2} R T_{0}

Total change in temperature from series

A

to

C

is

Δ T = 3 T_{0}

Therefore,
Molar heat capacity

= \frac{Δ Q}{Δ T} = \frac{\frac{19}{2} R T _{0}}{3 T _{0}} = \frac{19}{6} R

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

$\frac{13 R}{6}$

$\frac{19 R}{6}$

$\frac{23 R}{6}$

$\frac{17 R}{6}$

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

613R​

619R​

623R​

617R​

$\frac{13 R}{6}$

$\frac{19 R}{6}$

$\frac{23 R}{6}$

$\frac{17 R}{6}$