One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is $100 K$ and the universal gas constant $R =8.0 Jmol ^{-1} K ^{-1}$, the decrease in its internal energy, in Joule, is. . . . .
IIT 2018, Medium
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Adiabatic Expansion
$PV ^\gamma=\text { constant }$
$T . V ^{\gamma-1}=\text { constant }$
$T _2= T _1\left(\frac{ V _1}{ V _2}\right)^{\gamma-1} \text { where } \gamma=\frac{5}{3}$
$T _2= T _1\left(\frac{1}{8}\right)^{2 / 3}=\frac{ T _1}{4}=25 K$
$\Delta U =\frac{ f }{2} nR \Delta T =\frac{3}{2} \times 1 \times 8 \times 75=900 J$
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