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At 27°c ,a gas is compressed suddenly such that its pressure becomes 1/8th of its original pressure. Final temperature will be if gamma =5/3

At 27°c ,a gas is compressed suddenly such that its pressure becomes 1/8th of its original pressure. Final temperature will be if gamma =5/3

Grade:12th pass

2 Answers

Arun
25750 Points
6 years ago
Dear student
In an adiabatic process
PV\gamma = constant
P(nRT/P)\gamma = constant
P1-\gamma T\gamma = constant
Now
(P1/P2)1-\gamma/\gamma = T2/T1
Put the value and you will get the answer.
 
Regards
Arun (askIITians forum expert)
ankit singh
askIITians Faculty 614 Points
3 years ago
T^{\gamma}P^{1-\gamma} = constant
T_{1}^{\gamma}P_{1}^{1-\gamma}=T_{2}^{\gamma}P_{2}^{1-\gamma}
\dfrac{P_{1}^{1-\gamma}}{P_{2}^{1-\gamma}}=\dfrac{T_{2}^{\gamma}}{T_{1}^{\gamma}}
(\dfrac{P_{1}}{P_{2}})^{1-\gamma}=(\dfrac{T_{2}}{T_{1}})^{\gamma}
(\dfrac{P\times8}{P})^{1-\dfrac{5}{3}}=(\dfrac{T_{2}}{300})^{\dfrac{5}{3}}
T_{2}= 300\times((8)^{-\dfrac{2}{3}})^{\dfrac{3}{5}}
T_{2}= 130.58\ K
T_{2}= 130.58-273 = -142.42\ C
T_{2}=-142\ C

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