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in Thermal Physics by (54.5k points)
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A balloon partially filled with the gas volume 30 m3 at on surface of the earth where pressure is 76 cm of Hg and temperature is 27°C. What will be the increase in the volume of the gas balloon when it rises to a height where the temperature becomes (-54°C) and pressure become 7.6 cm of Hg.

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Given, P1 = 76 cm Hg, 

P2 = 7.6 cm of Hg 

V1 = 30 m3, V2 = ? 

T1 = 27 + 273 = 300 K 

T2 = -54 + 273 = 219 K

By gas equation

\(\frac{P_1V_1}{T_1} = \frac{P_2 V_2}{T_2}\)

V2 = \(\frac{P_1V_1T_2}{T_1P_2}\) = \(\frac{76 \times 30 \times 219}{300 \times 7.6}\) = 219 m3

So increase in volume of gas = 219 – 30 = 189 m3.

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