The molar specific heat at constant pressure of an ideal gas is (7/2)R. The ratio of specific heat at constant pressure to that at constant volume is :-

Question

The molar specific heat at constant pressure of an ideal gas is (7/2)R. The ratio of specific heat at constant pressure to that at constant volume is :- (A) 9/7 (B) 7/5 (C) 8/7 (D) 5/7

Tardigrade Admin · Accepted Answer

Molar specific heat at constant pressure CP=(7/2) R Since, CP-CV=R or, CV=CP-R=(7/2) R-R=(5/2) R ∴ (CP/CV)=((7 / 2) R/(5 / 2) R)=(7/5)

Q. The molar specific heat at constant pressure of an ideal gas is $(7/2) R$ . The ratio of specific heat at constant pressure to that at constant volume is :-

9/7

7/5

8/7

5/7

Molar specific heat at constant pressure
$C_{P} = \frac{7}{2} R$
Since, $C_{P} - C_{V} = R$
or, $C_{V} = C_{P} - R = \frac{7}{2} R - R = \frac{5}{2} R$
$∴ \frac{C _{P}}{C _{V}} = \frac{( 7/2 ) R}{( 5/2 ) R} = \frac{7}{5}$

Q. The molar specific heat at constant pressure of an ideal gas is (7/2)R. The ratio of specific heat at constant pressure to that at constant volume is :-

9/7

7/5

8/7

5/7

Molar specific heat at constant pressure CP​=27​R Since, CP​−CV​=R or, CV​=CP​−R=27​R−R=25​R ∴CV​CP​​=(5/2)R(7/2)R​=57​

Q. The molar specific heat at constant pressure of an ideal gas is $(7/2) R$ . The ratio of specific heat at constant pressure to that at constant volume is :-

Molar specific heat at constant pressure
$C_{P} = \frac{7}{2} R$
Since, $C_{P} - C_{V} = R$
or, $C_{V} = C_{P} - R = \frac{7}{2} R - R = \frac{5}{2} R$
$∴ \frac{C _{P}}{C _{V}} = \frac{( 7/2 ) R}{( 5/2 ) R} = \frac{7}{5}$