Ten kilograms of R410A contained in a pistoncyclinder assemb

Ten kilograms of R-410A contained in a piston-cyclinder assembly undergoes a process for which the pressure-specific volume relationship is PV^n = constant. The initial and final states of refrigerant are fixed to be 400kPa, -5 degrees C and 2000kPa, 70 degrees C respectively. Determine the work for the process in KJ.

Solution

given that the belocw relation:

PV^n = constant

so, we have

   P1V1^n = P2V2^n

Here, P1 = 400 kPa, P2 = 2000 kPa for these values, we have

          V1 = 0.0586 and V2 = 0.013

so,

   P1V1^n = P2V2^n

   400 kPa*0.0586^n = 2000 kPa*0.013^n

hence, n = 1.0688

hence,the work done is,

    W = m{[P1V1 - P2V2]/[n - 1]}

here, m = 10 kg and other data substitute in above equation and solve for W.

   W = -372.093 kJ