Which are true for reversible adiabatic process :

w = 2.303 R T log \frac{V_{2}}{V_{1}}

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w = \frac{n R}{(γ - 1)} (T_{2} - T_{1})

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w = 2.303 R T log \frac{V_{1}}{V_{2}}

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Δ U = w

n C_{v} Δ T

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Solution

The correct option is D $Δ U = w$ = $n C_{v} Δ T$
We know, from first law, $Δ U = q + w$ .
For adibatic process, $q = 0$ .
$w = Δ U$
Also $Δ U$ = $n C_{v} d T$
(using $C_{v} = \frac{R}{γ - 1}$ )
$Δ U = w = \frac{n R}{(γ - 1)} (T_{2} - T_{1})$ .
These are the derived formula for $W_{r e v}$ in adiabatic process.

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