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Standard XII

Physics

Work

A gas expands...

Question

A gas expands adiabatically from a temperature $T_{1}$ to a temperature $T_{2} (T_{1} > T_{2})$ . The work done in this process is

C_{p} (T_{1} - T_{2})

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C_{v} (T_{1} - T_{2})

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R (T_{1} - T_{2})

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Zero

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Solution

The correct option is C $C_{v} (T_{1} - T_{2})$
Work done in an adiabatic expansion is given by
$W = \frac{R}{γ - 1} [T_{1} - T_{2}] . . . . . (i)$
where, $T_{1} =$ initial temperature of the gas
$T_{2} =$ final temperature of the gas
$γ =$ adiabatic constant
$R =$ universal gas constant
Now, universal gas constant is given by:
$R = C_{p} - C_{v}$
Hence, equation (i) becomes
$W = \frac{C_{p} - C_{v}}{γ - 1} [T_{1} - T_{2}]$
Because, $γ = \frac{C_{p}}{C_{v}}$ , so we have
$W = \frac{C_{p} - C_{v}}{\frac{C_{p}}{C_{v}} - 1} [T_{1} - T_{2}]$
$W = \frac{C_{p} - C_{v}}{\frac{C_{p} - C_{v}}{C_{v}}} [T_{1} - T_{2}]$
or $W = C_{v} (T_{1} - T_{2})$ .

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A gas expands adiabatically from a temperature T1 to a temperature T2(T1>T2). The work done in this process is

A gas expands adiabatically from a temperature $T_{1}$ to a temperature $T_{2} (T_{1} > T_{2})$ . The work done in this process is