Assertion :At a given temperature the specific heat of a gas at constant volume is always greater than its specific heat at constant pressure. Reason: When a gas is heated at constant volume some extra heat is needed compared to that at constant pressure for doing work in expansion.

Statement-1 is false, Statement-2 is true.

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Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

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Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

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Statement-1 is true, Statement-2 is false

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Solution

The correct option is B Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
We use the relation for the first law of thermodynamics, which states that:
$Δ q = Δ U + w = Δ U + \int P d V$
and also $Δ q = n C Δ T$

for a constant volume process.
$Δ q = n C_{v} Δ T = Δ U + \int P (0)$
i.e. $n C_{v} Δ T = Δ U$

for a constant pressure process
$Δ q = n C_{p} Δ T = Δ U + \int P (d V)$
i.e. $n C_{p} Δ T = Δ U + \int P (d V)$

From the two relations we see that $C_{p}$ is always greater than $C_{v}$ because in a constant pressure process, work is done and part of the heat supplied goes into doing the work
Hence, both assertion and reason are true, and the reason is the correct explanation for the assertion

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