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  4. During an adiabatic compression, 830 J of work is done on 2 moles of a diatomic ideal gas to reduce its volume by 50 %. The change in its temperature is nearly: (R = 8.3 JK-1 mol-1)

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Q. During an adiabatic compression, $830\, J$ of work is done on $2$ moles of a diatomic ideal gas to reduce its volume by $50\%$. The change in its temperature is nearly : $(R = 8.3 JK^{-1}\, mol^{-1})$

JEE MainJEE Main 2014Thermodynamics

Solution:

The work done in adiabatic process is given as
$
W=\frac{n R \Delta T}{\gamma-1}
$
or
$830=\frac{2 \times 8.3 \times \Delta T}{1.4-1}$
$
\Delta T=20 K
$