Q101 / 150 · MHT CET 2022 (07 Aug Shift 1) · Physics

If $\mathrm{R}$ is universal gas constant the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from $273 \mathrm{~K}$ to $373 \mathrm{~K}$ when no work is done is

  • A
    $150 \mathrm{R}$
  • B
    $100 \mathrm{R}$
  • C
    $500 \mathrm{R}$
  • Correct answer
    D
    $300 \mathrm{R}$

Solution

For an ideal gas, the internal energy in only a function of the gas temperature and is a measure of the mean translational kinetic energy of the atoms. $\Delta \mathrm{Q}=\Delta \mathrm{U}+\Delta \mathrm{Q}=0 \Rightarrow \Delta \mathrm{Q}=\Delta \mathrm{U}=\frac{\mathrm{n}}{2} \mathrm{R} \Delta \mathrm{T}$ When $\mathrm{n}=$ degree of freedom for monoatomic gas i.e $=3$ $=\frac{3}{2} \times 2 \mathrm{R}(373-273)=300 \mathrm{R}$

Hence, the correct answer is option: 'D'.

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