Answer:
The resulting pressure of the gas when its volume decreases is 300 kN/m².
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
[tex]T = \frac{P_1V_1}{nR} \\\\T = \frac{150.kPa \ \times \ 80 .L}{0.5 .mol \ \times \ 8.315(L.kPa/mol.K)} \\\\T = 2,886.35 \ K[/tex]
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;
[tex]P_2V_2 = nRT\\\\P_2 = \frac{nRT}{V_2} \\\\P_2 = \frac{0.5 \times 8.315\times 2886.35}{40} \\\\P_2 = 300 \ kPa = 300 \ kN/m^2[/tex]
Therefore, the resulting pressure of the gas when its volume decreases is 300 kN/m².
