In a polytropic process an ideal gas (y= 1.40) was compressed from volume `V_1 = 10 litres to v_2 =5 litres`. The pressure increased from `p_1 = 10^(5) Pato p_(2) = 5xx10^(5)` Pa.Determine: (a) the polytropic expoment n, (b) the molar heat capacity of the gas for the process.

Answer

(a)2.32 (b)1.7R

Explanation

In a polytropic process `p V^(n) = k(a constant)`
`therefore p^(1)V_(1)^(n) = p_(2)V_(2)^(n) or (V_(1)/(V_(2)))^(n) = p_(2)/p_(1)`
or `n = (Inp_(2)//p_(1))/(InV_(1)//V_(2))`
Here `n =(In 5)/(In 2) = (1.6094)/(0.6931) = 2.32`
In a polytropic process
`C=(R)/(gamma-1) =(R)/(n-1) =(R)/(1.4-1)-(R)/(2.32-1) =1.74R`