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) 5/7 (b) 9/7 (c) 7/5 (d) 8/7

Answer 1

Given that, the molar specific heat at constant pressure of an ideal gas is (7/2)R.

We have to find the ratio of specific heat at constant pressure to that at constant volume.

Molar specific heat at constant pressure is 7/2 × R.

⇒ Cp = 7R/2 ...............(A)

Using Mayor's Formula:

Cp - Cv = R

Here-

• Cp is molar specific heat at constant pressure.
• Cv is molar specific heat at constant volume.
• R is universal gas constant.

Cp - Cv = R ..................(1st equation)

Substitute value of Cp in (1st equation)

→ 7R/2 - Cv = R

→ 7R/2 - R = Cv

→ (7R - 2R)/2 = Cv

→ 5R/2 = Cv .....................(B)

Ratio of ratio of specific heat at constant pressure to that at constant volume:

Divide (A) and (B)

→ Cp/Cv = (7R/2)/(5R/2)

→ Cp/Cv = (7R × 2)/(5R × 2)

→ Cp/Cv = 7/5

Therefore, the ratio of specific heat at constant pressure i.e. Cp to that at constant volume i.e. Cv is 7:5.

Option c) 7/5

Answer 2

✪ 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) 5/7 (b) 9/7 (c) 7/5 (d) 8/7

✪ Solution :-

(c) 7/5

✪ Explanation :-

Molar specific heat at constant pressure :-

$\sf{C_P=\dfrac{7}{2}R }$

We know,

$\bigstar\ \sf{C_P=R+C_V}$

$\sf{\implies C_V=C_P-R}\\\\\sf{\implies C_V=\dfrac{7R}{2}-R }\\\\\sf{\implies C_V=\dfrac{7R-2R}{2} }\\\\\sf{\implies C_V=\dfrac{5}{2}R }$

Dividing Cv from Cp :-

$\displaystyle{\sf{\frac{C_P}{C_V}=\frac{\frac{7}{2}R }{\frac{5}{2} R} }}\\\\\\\displaystyle{\sf{\implies \frac{C_P}{C_V}=\frac{7}{2}\div \frac{5}{2} }}\\\\\\\displaystyle{\sf{\implies \frac{C_P}{C_V}= \frac{7}{5} }}$

Hence,  the answer is (c) 7/5.