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A closed vessel $10 L$ in volume contains a diatomic gas under a pressure of $1 a t m$ . What amount of heat should be imparted to the gas to increase the pressure in the vessel five times?

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$10^{4} J$

$12300 J$

$625 J$

$10^{6} J$

answer is A.

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Detailed Solution

$V =$ constant

From

$p V = n R T,$

$V Δ p = n R (Δ T)$

$Q = n C_{V} Δ T$

$= n (\frac{5}{2} R) Δ T = \frac{5}{2} (V Δ p)$

$= \frac{5}{2} \times (10 \times 10^{- 7}) (4 \times 10^{5})$

$= 10^{4} J$

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