Answer to Question #188975 in Mechanical Engineering for Illy

Question

i. A fixed mass of gas has a pressure of 1.2 MPa and volume of 0.3 m3 and temperature of 100 oC . The pressure is changed to 400 kPa and the volume changed to 0.06 m3. Determine the new temperature?

 

ii. A mass of gas is stored in a cylinder. The gas is stored at a pressure of 1.2 MPa and the cylinder has a volume of 0.03 m3 and temperature of 100 oC , Find the mass of the gas. The characteristic gas constant for air is 300 Jkg−1K−1.

Answer 1

i. Using the general gas law we find

p₁V₁/T₁ = p₂V₂/T₂

where

p₁ = 1.2 x 10⁶ Pa

V₁ = 0.3 m³

p₂ = 400 x 10³ Pa

V₂ = 0.06 m³

T₁ = (100 + 273.15) K = 373.15 K

T₂ = (p₂V₂T₁) / (p₁V₁) = (400 x 10³ Pa x 0.06 m³ x 373.15 K) / (1.2 x 10⁶ Pa x 0.3 m³) = 24.88 K

ii. pV = nRT

1.2 x 10⁶ Pa x 0.03 m³ = m x 300 Jkg⁻¹K⁻¹ x 373.15 K

m = 0.322 kg