Thermodynamics

JEE Main level, single correct, medium

141 of 190

Question 141 of 190

A litre of dry air at STP expands adiabatically to a volume of 33 litres. If γ=1.40,\gamma =1.40, the work done by air is: (31.4=4.6555)\left({3}^{1.4}=4.6555\right) [Take air to be an ideal gas]

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Answer: (B) 90.5J90.5J

P1=1atm,T1=273K{P}_{1}=1atm,{T}_{1}=273K
P1V1γ=P2V2γ{P}_{1}{V}_{1}^{\gamma }={P}_{2}{V}_{2}^{\gamma }
P2=P1[V1V2]γ{P}_{2}={P}_{1}{\left[\dfrac{{V}_{1}}{{V}_{2}}\right]}^{\gamma }
=1atm(13)1.4=1atm{\left(\dfrac{1}{3}\right)}^{1.4}
Now work done
=P1V1−P2V2γ−1==\dfrac{{P}_{1}{V}_{1}-{P}_{2}{V}_{2}}{\gamma -1}=90.5J90.5J

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