A vessel containing nitrogen gas is supplied a heat of $498 \mathrm{~J}$, so as to raise the temperature of…

A vessel containing nitrogen gas is supplied a heat of $498 \mathrm{~J}$, so as to raise the temperature of the gas by $40^{\circ} \mathrm{C}$ at constant pressure. The mass of nitrogen gas in the vessel is (Molecular mass of nitrogen $=28 \mathrm{~g}$; Universal gas constant $=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )
  1. $18 \mathrm{~g}$
  2. $12 \mathrm{~g}$
  3. $20 \mathrm{~g}$
  4. $15 \mathrm{~g}$

Solution

$\begin{aligned} & \text { } \Delta \mathrm{Q}=\mathrm{nC}_{\mathrm{P}} \Delta \mathrm{T} \\ & \Rightarrow \Delta \mathrm{Q}=\frac{\mathrm{M}}{\mathrm{M}_0}\left(\frac{\mathrm{f}}{2}+1\right) \mathrm{R} \Delta \mathrm{T} \\ & \Rightarrow 498=\frac{\mathrm{M}}{28}\left(\frac{5}{2}+1\right)(8.3) \times 40 \\ & \Rightarrow 498=\frac{M}{28} \times \frac{7}{2} \times 8.3 \times 40 \\ & \Rightarrow \mathrm{M}=12 \mathrm{~g} \\ & \end{aligned}$

Asked in: AP EAMCET 2022 (06 Jul Shift 1)

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