Question

A certain gas occupies a volume of 3.7 L at a pressure of 0.91 atm and a temperature of 283 K. It is compressed adiabatically to a volume of 0.85 L. Determine (a) the final pressure and (b) the final temperature, assuming the gas to be an ideal gas for which γ = 1.4.

Answer 1

Answer:

(a)

P₂ = 7.13 atm

(b)

T₂ = 157.14 K

Explanation:

(a)

V₁ = initial volume = 3.7 L = 3.7 x 10⁻³ m³

V₂ = final volume = 0.85 L = 0.85 x 10⁻³ m³

P₁ = Initial Pressure of the gas = 0.91 atm = 0.91 x 101325 = 92205.75 Pa

P₂ = Final Pressure of the gas = ?

Using the equation

$P_{1} V{_{1}}^{\gamma } = P_{2} V{_{2}}^{\gamma }$

$(92205.75) (3.7\times 10^{-3})^{1.4 } = P_{2} (0.85\times 10^{-3})^{1.4 }$

$P_{2}$ = 722860 Pa

$P_{2}$ = 7.13 atm

(b)

T₁ = initial temperature =283 K

T₂ = Final temperature = ?

using the equation

$P{_{1}}^{1-\gamma } T{_{1}}^{\gamma } = P{_{2}}^{1-\gamma } T{_{2}}^{\gamma }$

$(92205.75)^{1-1.4 } (283)^{1.4 } = (722860)^{1-1.4 } T{_{2}}^{1.4 }$

T₂ = 157.14 K