JEE Advanced · 2009 · 12 Apr 2009 · Paper 1 · Heat & Thermodynamics

C_{v}

and

C_{p}

denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then

(A) $C_{p} - C_{v}$ is larger for a diatomic ideal gas than for a monoatomic ideal gas
(B) $C_{p} + C_{v}$ is larger for a diatomic ideal gas than for a monoatomic ideal gas✓ Correct
(C) $C_{p} / C_{v}$ is larger for a diatomic ideal gas than for a monoatomic ideal gas
(D) $C_{p} \cdot C_{v}$ is larger for a diatomic ideal gas than for a monoatomic ideal gas✓ Correct

Answer: (B), (D)

Solution

For an ideal gas,

C_{p} - C_{v} = R

(same for both monoatomic and diatomic). For monoatomic:

C_{v} = \frac{3}{2} R

C_{p} = \frac{5}{2} R

. For diatomic:

C_{v} = \frac{5}{2} R

C_{p} = \frac{7}{2} R

. (A)

C_{p} - C_{v} = R

for both (equal, not larger). (B) For monoatomic:

C_{p} + C_{v} = 4 R

; for diatomic:

C_{p} + C_{v} = 6 R

(diatomic is larger). (C) For monoatomic:

γ = \frac{5}{3} \approx 1.67

; for diatomic:

γ = \frac{7}{5} = 1.4

(monoatomic is larger). (D) For monoatomic:

C_{p} \cdot C_{v} = \frac{15}{4} R^{2}

; for diatomic:

C_{p} \cdot C_{v} = \frac{35}{4} R^{2}

(diatomic is larger). Therefore, (B) and (D) are correct.

JEE Advanced · 2009 · 12 Apr 2009 · Paper 1 · One or more correct options