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

(a)

P₂ = 7.13 atm

(b)

T₂ = 157.14 K

Step-by-step 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* 10^(-3))^(1.4 ) = P_(2) (0.85* 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