Question

Work done in an adiabatic system. Derivation. ​

Answer 1

Adiabatic Process. An adiabatic process is one in which no heat is gained or lost by the system. The first law of thermodynamics with Q=0 shows that all the change in internal energy is in the form of work done. ... This condition can be used to derive the expression for the work done during an adiabatic process.

Answer 2

For an adiabatic process of ideal gas equation we have

    PVγ = K (Constant)               (14)

Where γ is the ratio of specific heat (ordinary or molar) at constant pressure and at constant voluume

    γ = Cp/Cv

Suppose in an adiabatic process pressure and volume of a sample of gas changs from (P1, V1) to (P2, V2) then we have

    P1(V1)γ=P2(V2)γ=K

Thus, P = K/Vγ

Work done by gas in this process is

    W = ∫PdV

where limits of integration goes from V1 to V2

Putting for P=K/Vγ, and integrating we get,

    W = (P1V1-P2V2)/(γ-1)          (16)

In and adiabatic process if W>0 i.e., work is done by the gas then T2< T1

If work is done on the gas (W<0) then T2 > T1 i.e., temperature of gas rises.