Air initially at 140 kPa and 375 K undergoes a polytropic st

Air, initially at 140 kPa and 375 K undergoes a polytropic state change to 238 kPa and 412.5 K. What is the polytropic exponent of this process?

Solution

>> As Polytropic Process is :

PVⁿ = constant, ....(1)....

where, n = Polytropic Exponent

As, Ideal gas Equation is : PV = nRT

So, Eq. (1). also becomes :

Tⁿ/P^n-1 = c

>> Now here, P1 = 140 kPa and T1 = 375 K

and, P2 = 238 kPa , T2 = 412.5 K

>> Putting above as ,

T1ⁿ/P1^n-1 = T2ⁿ/P2^n-1

=> (T2/T1) = (P2/P1)^(n-1)/n

=> (412.5/375) = (238/140)^(n-1)/n

=> 1.1 = 1.7^(n-1)/n

Taking ln both sides,

=> ln(1.1) = (n-1)/n * ln(1.7)

=> (n-1)/n = 0.1796

Solving,

=> n = 1.219 ......POLYTROPIC EXPONENT.......