JEE Advanced 2018 · Paper 2 · Physics Q12

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PhysicsNumerical+3Question 12 of 54

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 $R = 8.0\ \mathrm{J\,mol^{-1}\,K^{-1}}$ , the decrease in its internal energy, in Joule, is__________.

Your answer

Answer and worked solution

Official answer: 900

Final temperature. For a monatomic gas, $\gamma=\tfrac53$ and $TV^{2/3}$ is constant:
$T_2=100\times\left(\frac18\right)^{2/3}=\frac{100}4=25\text{ K}.$

Decrease in internal energy.
$\Delta U=nC_v\Delta T=1\times\frac32\times8\times75=900\text{ J}.$

Answer: 900

Topics:Thermodynamic processes First law and internal energy

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JEE Advanced 2018 · Paper 2, Physics question 12