I'm a little confused with deriving a formula for the work you need to adiabatically compress a gas. It's been a while since my thermodynamics course, but i seem to remember two possible ways of doing this.
My first approach is: work is the pressure integrated over Volume : W = int(pdV), and assuming that pV^K = Constant (where K is the specific heat ratio), this yields
W = 1/(K-1)*(P2*V2 - P1*V1)
The second approach is by using the energy equation. A change in specific enthalpy (delta_h) is equal to Cp*(T2-T1) with Cp the specific heat at constant pressure. This change in enthalpy should equal the compression work since heat flow (q) is zero. With Cp = K/(K-1) * R (R = gas constant) en pV = RT, this yields
W = K/(K-1)*(P2*V2-P1*V1)
The two approaches differ by K.. The site of Wolfram Alpha gives the first formula for the work of an adiabatic compression, while my course on pneumatics says it's the second one. What is the difference between the two?
Thanks!
I'm a little confused with deriving a formula for the work you need to adiabatically compress a gas. It's been a while since my thermodynamics course, but i seem to remember two possible ways of doing this.
My first approach is: work is the pressure integrated over Volume : W = int(pdV), and assuming that pV^K = Constant (where K is the specific heat ratio), this yields
W = 1/(K-1)*(P2*V2 - P1*V1)
The second approach is by using the energy equation. A change in specific enthalpy (delta_h) is equal to Cp*(T2-T1) with Cp the specific heat at constant pressure. This change in enthalpy should equal the compression work since heat flow (q) is zero. With Cp = K/(K-1) * R (R = gas constant) en pV = RT, this yields
W = K/(K-1)*(P2*V2-P1*V1)
The two approaches differ by K.. The site of Wolfram Alpha gives the first formula for the work of an adiabatic compression, while my course on pneumatics says it's the second one. What is the difference between the two?
Thanks!
