2
Question
10 L of a monoatomic ideal gas at 0oC and 5 atm is suddenly released to 1 atm pressure and the gas is expanded adiabatically against the constant pressure. Find the final volume (in L) of the gas.
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Solution
The correct option is C 34 L
For an adiabatic process q=0,
From the First law, ΔU=q+w
For an adiabatic irreversible process, w=−Pext(V2−V1)
w=△U=P2V2−P1V1γ−1
⇒−Pext(V2−V1) = P2V2−P1V1γ−1
For a monoatomic gas, γ = 1.67
putting all the values,
⇒−1(V2−10) = 1×V2−5×10γ−1
⇒10−V2 = V2−500.67
⇒(10−V2)×0.67=(V2−50)
⇒V2= 34 L
For an adiabatic process q=0,
From the First law, ΔU=q+w
For an adiabatic irreversible process, w=−Pext(V2−V1)
w=△U=P2V2−P1V1γ−1
⇒−Pext(V2−V1) = P2V2−P1V1γ−1
For a monoatomic gas, γ = 1.67
putting all the values,
⇒−1(V2−10) = 1×V2−5×10γ−1
⇒10−V2 = V2−500.67
⇒(10−V2)×0.67=(V2−50)
⇒V2= 34 L
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