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If a gas (y=1.5) is compressed at pressure 27 times the initia

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If a gas $(y = 1.5)$ is compressed at pressure $27$ times the initial pressure, then calculate the change in temperature if the initial temperature is $27^{o} C$

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If a gas

(y = 1.5)

is compressed at pressure

27

times the initial pressure, then calculate the change in temperature if the initial temperature is

27^{o} C

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

Given,

y = 1.5; P_{1} = P; P_{2} 27 P

T_{1} 27 + 273 = 300 k; T_{2} = ?

∴

Relation between pressure and temperature in an adiabatic process

\frac{T ^{γ}}{P ^{γ - 1}} = co n s t an t

∴ \frac{T _{2}^{γ}}{P _{2}^{γ - 1}} = \frac{T _{1}^{γ}}{P _{1}^{γ - 1}} \Rightarrow (\frac{T _{2}}{T _{1}})^{γ} = (\frac{P _{2}}{P _{1}})^{γ - 1}

\frac{T _{2}}{T _{1}}

= (\frac{P _{2}}{P _{1}})^{\frac{γ - 1}{γ}} =

(\frac{27 P}{P})^{\frac{1.5 - 1}{1.5}}

= (27)^{\frac{1}{3}}

\frac{T _{2}}{T _{1}} = 3

∴ T_{2} = 3 \times T_{1} = 3 \times 300 = 900 K

T_{2} = 900 - 273 = 62 7^{o} C

Change in temperature

∴ Δ T = T_{2} - T_{1} = 627 - 27

60 0^{o} C

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Question Text	If a gas $(y = 1.5)$ is compressed at pressure $27$ times the initial pressure, then calculate the change in temperature if the initial temperature is $27^{o} C$
Answer Type	Text solution:1
Upvotes	150