Question

A gas is taken in a cylinder. The walls of the cylinder is insulated from the surroundings

1. The gas in a cylinder is suddenly compressed. Which thermo dynamic process involves in this statement. Explain the thermo dynamic process.

2.  If gas is suddenly compressed to 1/4^th of its, original volume. Calculate the rise in temperature. The initial temperature was 27°C and γ = 1.5.

Answer 1

1. Adiabatic. A thermo dynamic process in which no heat enters or leaves the system.

2. T. = 27°C = 27 + 273 = 300k

\(\frac{V_1}{V_2}= \frac{V}{v/4} = 4\)

\(T_1 V_1^{γ-1} = T_2 V_2^{γ-1}\)

\(T_2 = T_1[\frac{V_1}{V_2}]^{γ-1}\)

= 300 × 4^{1.5 – 1}

= 300 × 4^1/2

= 600K

rise in temperature = 600K – 300K = 300K.