Question

A closed vessel of volume 80 litres contains 0.5 N of gas at a pressure of 150 kN/m2. If the gas is compressed isothermally to half its volume, determine the resulting pressure.

Answer 1

The resulting pressure of the gas when its volume decreases is 300 kN/m².

Step-by-step explanation:

Given;

initial volume of the gas, V₁ = 80 L

number of moles of the gas, n = 0.5 moles

initial pressure of the gas, P₁ = 150 kN/m² = 150 kPa

Determine the constant temperature of the gas using ideal gas equation;

PV = nRT

where;

R is ideal gas constant = 8.315 L.kPa/K.mol

T is the constant temperature

`T = (P_1V_1)/(nR) \\\\T = (150.kPa \ * \ 80 .L)/(0.5 .mol \ * \ 8.315(L.kPa/mol.K)) \\\\T = 2,886.35 \ K`

When the gas is compressed to half of its volume;

new volume of the gas, V₂ = ¹/₂ V₁

= ¹/₂ x 80L = 40 L

The new pressure, P₂ is calculated as;

`P_2V_2 = nRT\\\\P_2 = (nRT)/(V_2) \\\\P_2 = (0.5 * 8.315* 2886.35)/(40) \\\\P_2 = 300 \ kPa = 300 \ kN/m^2`

Therefore, the resulting pressure of the gas when its volume decreases is 300 kN/m².