A rigid diatomic ideal gas is compressed adiabatically to (1/32) of its initial volume. If the initial temperature of the gas is T₁ (in kelvin) and the final temperature is " nT₁ ", the value of n is = 1.4

Step-by-step solution

For an adiabatic process, the relation between temperature and volume is given by: T₁ V₁^ - 1 = T₂ V₂^ - 1 Given that V₂ = V₁ 32 , T₂ = nT₁ , and = 1.4 , we can substitute these values into the equation: T₁ V₁^ 1.4 - 1 = nT₁ ( V₁ 32 )^ 1.4 - 1 V₁^ 0.4 = n ( V₁ 32 )^ 0.4 1 = n ( 1 32 )^ 0.4 n = (32)^ 0.4 Since 0.4 = 2 5 and 32 = 2^5 , we have: n = (2^5)^ 2 5 = 2^2 = 4 Answer: 4