A gas is enclosed in a thermally insulating container. Initially its volume is 800 cm³ and temperature is 27°C. It is adiabatically compressed to 200 cm³. Take γ = 1.5. The change in temperature is:
Options

Question

A gas is enclosed in a thermally insulating container. Initially its volume is 800 cm³ and temperature is 27°C. It is adiabatically compressed to 200 cm³. Take γ = 1.5. The change in temperature is:

Options

G1 Physics · Accepted Answer

Initial temperature: T₁ = 27°C = 300 K. For an adiabatic process, T V ( γ − 1 ) V^(γ-1) V ( γ − 1 ) = constant. Therefore, T₂/T₁ = (V₁/V₂)^(γ-1). Here, V₁/V₂ = 800/200 = 4, γ-1 = 0.5. Hence, T₂/T₁ = 4^0.5 = 2, so T₂ = 600 K. The question asks for the change in temperature: ΔT = T₂-T₁ = 600-300 = 300 K. Correct option: B.