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First Law of Thermodynamics

An ideal gas ...

Question

An ideal gas $(C_{v} = \frac{3}{2} R)$ is maintained in a vessel of volume $83 \times 10^{- 4} m^{3}$ at pressure $1.6 \times 10^{6} N m^{- 2}$ and temperature $300 K$ . If $2.49 \times 10^{4} J$ heat is given to this vessel, then its final temperature will be

A

600 K

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B

625 K

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C

650 K

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D

675 K

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Solution

The correct option is D $675 K$
$Q = n C_{v} d T ⟹ 2.49 \times 10^{4} = \frac{P V}{R T} \times (C_{v}) \times (T_{2} - T_{1})$

$2.49 \times 10^{4} = \frac{83 \times 10^{- 4} \times 1.6 \times 10^{6}}{8.314 \times 300} \times (1.5 \times 8.314) (T_{2} - 300)$

$T_{2} - 300 = 375 ⟹ T_{2} = 675 K$

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