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Question

Assertion :$$C_{P} - C_{V} = R$$ for an ideal gas. Reason: $$\left (\dfrac {\partial E}{\partial V}\right )_{T} = 0$$ for an ideal gas.


A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
$$C_v={(\cfrac{\partial E}{\partial T})}_v\longrightarrow 1$$
For an ideal gas, $$C_p-C_v=R$$
From $$(1) no.$$ Equation, $${ (\cfrac { \partial C_{ v } }{ \partial v } ) }_{ T }={ (\cfrac { \partial  }{ \partial v } { (\cfrac { \partial E }{ \partial T } ) }_{ v }) }_{ T }={ (\cfrac { \partial  }{ \partial T } { (\cfrac { \partial E }{ \partial v } ) }_{ T }) }_{ v }$$
For an ideal gas $${(\cfrac { \partial E }{ \partial v } )}_T=0$$
$$\Longrightarrow { (\cfrac { \partial C_{ v } }{ \partial v } ) }_{ T }={ (\cfrac { \partial  }{ \partial T } (0)) }_{ v }=0$$
But due to this $$C_P-C_v=R$$ is not reasoned.

Chemistry

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