(2 pts) Equation (3.25) in the textbook shows how to calculate the work from an adiabatic process of\ an ideal gas system based on the change of internal energy.\

W=\\\\Delta U^(ig)=C_(V)^(ig)\\\\Delta T

\ This equation is transformed into (3.26) in which measurable properties

P,V^(g),T,C_(p),C_(v)

are used.\

W=(RT_(2)-RT_(1))/(\\\\gamma -1)=(P_(2)V_(2)^(ig)-P_(1)V_(1)^(ig))/(\\\\gamma -1)

\ Another equation (3.27) is then derived from (3.26) for work calculation.\

W=(P_(1)V_(1)^(ig))/(\\\\gamma -1)[((P_(2))/(P_(1)))^((\\\\gamma -1)/(\\\\gamma ))-1]=(RT_(1))/(\\\\gamma -1)[((P_(2))/(P_(1)))^((\\\\gamma -1)/(\\\\gamma ))-1]

\ (a) Please show in detail how (3.27) is derived from (3.26)\ (b) Please mark the applicability constraints of each equation in following table.

5. (2 pts) Equation (3.25) in the textbook shows how to calculate the work from an adiabatic process of an ideal gas system based on the change of internal energy. W=Uig=CVigT This equation is transformed into (3.26) in which measurable properties P,Vig,T,Cp,Cv are used. W=1RT2RT1=1P2V2igP1V1ig Another equation (3.27) is then derived from (3.26) for work calculation. W=1P1V1ig[(P1P2)(1)/1]=1RT1[(P1P2)(1)/1] (a) Please show in detail how (3.27) is derived from (3.26) (b) Please mark the applicability constraints of each equation in following table