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A spherical balloon is filled with an ideal mono-atomic gas. At some instant its pressure was P0, volume V0 and temperature T0. If the balloon expanded in such a manner so that the rate of radiation from the balloon remained constant. It was found that the work done by gas inside the balloon was 6P0V01−1n when its volume increased to 8V0.Find the value of n. (Assume ambient temperature to be close to 0 K)

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answer is 2.

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Detailed Solution

Rate of radiation = σeAT4= constantor r2T4 = constantor 43πr3T6 = constantor VT6=Cor TV1/6 = constant (1)Comparing it with polytropic equation TVK−1 = constantWe get K−1=16⇒ K=76 Work done by gas = nRT1−T2K−1=nR(1/6)T0−T2 =6nRT0−T02=6nRT01−12T2=T02 according to (1) = 6P0V01−12So n = 2

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A spherical balloon is filled with an ideal mono-atomic gas. At some instant its pressure was P0, volume V0 and temperature T0. If the balloon expanded in such a manner so that the rate of radiation from the balloon remained constant. It was found that the work done by gas inside the balloon was 6P0V01−1n when its volume increased to 8V0.Find the value of n. (Assume ambient temperature to be close to 0 K)