The amount of heat needed to raise the temperature

Question:

The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from $0^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ when no work is done is_______ . $R$ is the universal gas constant)

  1. $250 R$

  2. $750 \mathrm{R}$

  3. $175 \mathrm{R}$

  4. $500 \mathrm{R}$


Correct Option: , 4

Solution:

$\Delta \mathrm{Q}=\Delta \mathrm{U}+\Delta \mathrm{W}$

Here $\Delta W=0$

$\Delta \mathrm{Q}=\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}$

$\Delta Q=4 \times \frac{5 R}{2}(50)=500 \mathrm{R}$

Hence option (4).

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