During a compression at a constant pressure of 290 Pa, the volume of an ideal gas decreases from 0.62 m3 to 0.21 m3. The initial temperature is 320 K, and the gas loses 160 J as heat. What are (a) the change in the internal energy of the gas and (b) the final temperature of the gas?

a) - 41.1 Joule

b) 108.38 Kelvin

Explanation:

Pressure = P = 290 Pa

Initial volume of gas = V₁ = 0.62 m³

Final volume of gas = V₂ = 0.21 m³

Initial temperature of gas = T₁ = 320 K

Heat loss = Q = - 160 J

Work done = PΔV

⇒Work done = 290 * (0.21-0.62)

⇒Work done = - 118.9 J

a) Change in internal energy = Heat - Work

ΔU = - 160 - (-118.9)

⇒ΔU = - 41.1 J

∴ Change in internal energy is - 41.1 J

b) V₁/V₂ = T₁/T₂

⇒T₂ = T₁V₂/V₁

⇒T₂ = 320*0.21/0.62

⇒T₂ = 108.38 K

∴ Final temperature of the gas is 108.38 Kelvin