Thermodynamis Section 4 - Isothermal Expansion

what is isothermal expansion

hen a system exchanges work with its surroundings which is a pressure reservoir at the same temperature as the system

why cant we calculate work done in irreversible isothermal expansion using dW= PsdV

because the pressure of the system Ps is not well defined at any point in the irreversible process

how do we calculate work in irreversible isothermal expansion

work done by system = work done on surroundings = integral from V2 to V1 (PxA)dx = integral from V2 to V1 PxdV = P2(V2-V1).

what is Px and Ps

Px is pressure of the reservoir and Ps is pressure of the system

how do we make isothermal expansion reversible

apply a force that is dP lower than what is needed to balance the system pressure and take infinitely long to let volume expand while keeping apparatus in thermal contact with a temperature bath

how is work calculated for reversible isothermal expansion

W by system = nRT integral from V2 to V1 dV/V = nRT ln(V2/V1) or we can use dW on surroundings = PxdV = (Ps - dP_dV = PsdV -dPdV = PsdV

how does work compare in reversible and irreversible isothermal expansion

more work is done in reversible process

how do you interpret an isotherm graph

plot P vs V, area under curve between V2 and V1 is work done on surroundings in reversible, the area under curve between V2 and V1 and P2 and P1 is lost work due to irreversibility and the first minus the second is the irreversible work .The slope is expansion and the two lines bringing back to original point is compression.

what can u conclude from the equation for reversible isothermal expansion

d(dash)W= PdV

what does d(dash) mean

that the differential is an inexact differential as the parameter is path dependent

what is the effect of the d(dash)

we cant write W= integral from 2 to 1 dW = [W]2 to 1