Statement I: Change in internal energy of a system containing mole of ideal gas can be written as

Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Statement I: Change in internal energy of a system containing $n$ mole of ideal gas can be written as

$Δ U = n C_{v} (T_{f} - T_{i}) = \frac{n R}{γ - 1} (T_{f} - T_{i}),$ where $γ = \frac{C_{p}}{C_{v}}, T_{i} = initial temperature, T_{f} =$ final temperature.

Statement II: Relation between degree of freedom $f$ and $γ (= \frac{C_{p}}{C_{v}})$ is $(γ = 1 + \frac{2}{f}) .$

Choose the correct answer from the options given below [2026]

Smart Achievers · Accepted Answer

(2)

$Δ U = n C_{v} (T_{f} - T_{i}) = \frac{n R}{γ - 1} (T_{f} - T_{i})$

$γ = \frac{C_{p}}{C_{v}} = \frac{(\frac{f}{2} + 1) R}{\frac{f}{2} R} =$ $1 + \frac{2}{f}$

Solution

1 Both A and R are true and R is the correct explanation of A

2 Both A and R are true but R is NOT the correct explanation of A

3 A is true but R is false

4 A is false but R is true

Ans.
(2)

$Δ U = n C_{v} (T_{f} - T_{i}) = \frac{n R}{γ - 1} (T_{f} - T_{i})$

$γ = \frac{C_{p}}{C_{v}} = \frac{(\frac{f}{2} + 1) R}{\frac{f}{2} R} =$ $1 + \frac{2}{f}$

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