We know that in adiabatic expansion, there is no heat exchange. So, ∆Q=0. From the first law of thermodynamics: ∆Q=∆U+W Since ∆Q=0, this means: 0=∆U+W So, W=−∆U The change in internal energy for n moles of a diatomic gas is: ∆U=nCV∆T where CV for a diatomic gas is ‌
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R. Here, n=3 moles and the temperature change ∆T=−50∘C (or -50 in Kelvin, since the size of the degree is the same). So, W=−∆U=−nCV∆T=−3×‌
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R×(−50) Multiplying out: −3×‌
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R×(−50)=7.5R×50=375R The work done by the gas is 375R.