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Ideal Gas Equation

To what press...

Question

To what pressure must a certain ideal gas $(γ = 1.4)$ at $373 K$ and $1$ atmospheric pressure be compressed adiabatically in order to raise its temperature to $773 K$ ?

7.89 a t m

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79 a t m

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7.1 a t m

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6.89 a t m

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Solution

The correct option is A $7.89 a t m$
Given $γ = 1.4$ for a adiabetic process $⟹ P^{1 - γ} T^{γ} = c o n s t a n t$
$P_{1},$ initial pressure, $P_{1} = 1$ atm; let $P_{2} = P$
Temperature, $T_{1} = 373 K$ and $T_{2} = 673 K$
$(\frac{P_{1}}{P_{2}})^{1 - γ} = (\frac{T_{2}}{T_{1}})^{γ}$
${(\frac{1}{P})}^{1 - 1.4} = {(\frac{673}{373})}^{1.4} P = 7.89 a t m$
Gas has to compressed to a final pressured $7.89 a t m$ .

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To what pressure must a certain ideal gas (γ=1.4) at 373K and 1 atmospheric pressure be compressed adiabatically in order to raise its temperature to 773K?

The correct option is A 7.89 atmGiven γ=1.4 for a adiabetic process ⟹P1−γTγ=constantP1, initial pressure, P1=1 atm; let P2=PTemperature, T1=373K and T2=673K(P1P2)1−γ=(T2T1)γ(1P)1−1.4=(673373)1.4P=7.89atmGas has to compressed to a final pressured 7.89atm.

To what pressure must a certain ideal gas $(γ = 1.4)$ at $373 K$ and $1$ atmospheric pressure be compressed adiabatically in order to raise its temperature to $773 K$ ?