Question

A container with initial volume of 1.7 m³ and pressure of 100 kPa is adiabatically compressed to a volume of 0.6 m³. What is the final pressure? Give your answer as a whole number in units of kPa.

Answer 1

$\gamma$ = 1.4

Initial volume = V₁ = 1.7 m³

Initial pressure = P₁ = 100 kPa = 1 x 10⁵ Pa

Final volume = V₂ = 0.6 m³

Final pressure = P₂

The process is adiabatic.

$P_{1}V_{1}^{\gamma } = P_{2}V_{2}^{\gamma }$

$(1\ast 10^{5})(1.7)^{1.4} = P_{2}(0.6)^{1.4}$

P₂ = 4.2975 x 10⁵ Pa

P₂ = 429.75 kPa

Final pressure = 429.75 kPa