A balloon containing an ideal gas has a volume of l0 litre and temperature of $l 7^{o}$ . If it is heated slowly to 75"C, the work done by the gas inside the balloon is (neglect elasticity of the balloon and take atmospheric pressure as $l 0^{5}$ Pa)

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100 J

200 J

250 J

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answer is B.

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Detailed Solution

Since elasticity of balloon is negligible, pressure inside balloon pressure outside balloon = $P_{atm}$

$∴ W = P_{atm} ∆ V$

$V_{in} = 10 litre$

$\frac{V_{in}}{T_{in}} = \frac{V_{fin}}{T_{fin}} \Rightarrow V_{final} = (\frac{V_{in} T_{final}}{T_{in}}) litre$

$\Rightarrow W = P_{atm} V_{in} (\frac{T_{final}}{T_{in}} - 1)$

$\Rightarrow 10^{5} \times 10^{- 2} (\frac{58}{290}) = 200 J$

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