ThermodynamicsMedium

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 $\Delta U = {nC}_{v}\left( T_{f} - T_{i} \right) = \frac{nR}{\gamma - 1}\left( {\text{ }T}_{f} - T_{i} \right)$,

where $\gamma = \frac{C_{P}}{C_{v}},T_{i} =$ initial temperature, $T_{f} =$ final temperature.

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

Choose the correct answer from the options given below

Options

A.Both $\mathbf{A}$ and $\mathbf{R}$ are true and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$
B.Both $\mathbf{A}$ and $\mathbf{R}$ are true but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$
C.$\mathbf{A}$ is true but $\mathbf{R}$ is false
D.$\mathbf{A}$ is false but $\mathbf{R}$ is ttue

Solution

Sol. [Key Concept: Both statements are individually correct, but the degrees-of-freedom relation for $\gamma$ does not explain the $\Delta\ U$ expression.]

Both statements are correct but between does not explain the statement-1

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