Assertion : $C_{P} - C_{V} = R$ for ideal gas. Reason: $R$ is the work done when temperature of one mole of an ideal gas is increased by $1^{o}$ .

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
$C_{P} - C_{V} = R$
Mechanical work due to the expansion of one mole of gas is given by $P V = R T$ .

When the temperature is increased by $1^{o} C$ , the mechanical work done will be $P V = R$ .

$∵ T_{2} - T_{1} = 1^{0} C$

Hence, option A is correct.

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