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in Thermal Physics by (54.5k points)
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When a gas filled in a closed vessel is heated through 1°C, its pressure increases by 0.4% what is the initial temperature of the gas?

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Initial pressure P1 = P

Final pressure P2 = P + \(\frac{0.4P}{100}\)

T1 = T, T2 = T + 1

At constant volume \(\frac{P_2}{P_1}\) = \(\frac{T_2}{T_1}\)

\(\frac{P(1+ 0.004)}{P}\) = \(\frac{T - 1}{T}\)

PT + 0.004 PT = PT + P

0.004PT = P

∴ T = \(\frac{1}{0.004}\) 

= 250 K

∴ Initial Temperature of the gas = 250 K

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