An ideal gas at 27^ C is compressed adiabatically to ( 8 27 ) of its original volume. If = 5/3 , then the rise in temperature of a gas is

Step-by-step solution

For an adiabatic process, the relation between temperature and volume is given by T V^ - 1 = constant . T₁ V₁^ - 1 = T₂ V₂^ - 1 Given T₁ = 27^ C = 300 K , V₂ = 8 27 V₁ , and = 5 3 . T₂ = T₁ ( V₁ V₂ )^ - 1 T₂ = 300 ( 27 8 )^ 5 3 - 1 T₂ = 300 ( 27 8 )^ 2 3 T₂ = 300 ( 3 2 )^2 = 300 9 4 = 675 K The rise in temperature is T = T₂ - T₁ = 675 K - 300 K = 375 K . Answer: 375 K