To raise the temperature of a certain mass of gas by 50 ∘ C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100 ∘ C at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

Δ Q = n C p Δ T ⇒ 160 = n C p 50 Δ Q = n C v Δ T ⇒ 240 = n C v 100 ⇒ C p C v = 16 5 * 10 24 = 4 3 ⇒ 1 + 2 f = 4 3 ⇒ f = 6

To raise the temperature of a certain mass of gas by $50^{\circ} C$ at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by $100^{\circ} C$ at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

Option 1 - 7

Option 2 - 5

Option 3 - 3

Option 4 - 6

3 Views|Posted 6 months ago

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Alok Kumar Singh | Contributor-Level 10

6 months ago

Correct Option - 4

Detailed Solution:

$Δ Q = {n C}_{p} Δ T \Rightarrow 160 = {n C}_{p} 50$

$Δ Q = {n C}_{v} Δ T \Rightarrow 240 = {n C}_{v} 100$

$\begin{array}{r} \Rightarrow \frac{C_{p}}{C_{v}} = \frac{16}{5} * \frac{10}{24} = \frac{4}{3} \\ \Rightarrow 1 + \frac{2}{f} = \frac{4}{3} \Rightarrow f = 6 \end{array}$

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Physics Thermodynamics 2025

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