MCQ
$2$ mole of $N_2$ gas at $27\,^oC$ is mixed with $1$ mole $He$ gas at $-73\,^oC$. Find $T_{mix}$ of the mixture
  • A
    $277\,^oC$
  • $277\,K$
  • C
    $5\,^oK$
  • D
    $50\,^oC$

Answer

Correct option: B.
$277\,K$
b
$\mathrm{T}_{\operatorname{mix}}=\frac{\mathrm{n}_{1} \mathrm{C}_{\mathrm{v}_{1}} \mathrm{T}_{1}+\mathrm{n}_{2} \mathrm{C}_{\mathrm{V}_{2}} \mathrm{T}_{2}}{\mathrm{n}_{1} \mathrm{C}_{\mathrm{V}_{1}}+\mathrm{n}_{2} \mathrm{C}_{\mathrm{V}_{2}}}$

$=\frac{2 \times \frac{5}{2} \mathrm{R} \times 300+1 \times \frac{3 \mathrm{R}}{2} \times 200}{2 \times \frac{5 \mathrm{R}}{2}+1 \times \frac{3 \mathrm{R}}{2}}=277 \mathrm{K}$

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