Isothermal Process - Thermodynamic Process | Physics Grade XI

Thermodynamic Process

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Isothermal Process - Thermodynamic Process | Physics Grade XI

Isothermal Process - Thermodynamic Process

Isothermal process 
The process in which the thermodynamic system undergoes a change in pressure and volume while the temperature remains constant is called isothermal process. There is a free exchange of heat from the system to its surrounding in this system.

CompressionExpansion

Isothermal ProcessApplication of First law to Isothermal Process

From the first law, we have
    dQ = dU + dW
 
Temperature in an isothermal process does not change, the change in internal energy of a gas is null because it only depends upon the temperature. So,
    dU = 0
    dQ = dU + dW
    dQ = 0 + dW
    dQ = dW = P dV

Thus, during isotheral process, heat supplied to the system = work done by the system

Work done during the Isothermal Process
Consider n-mole of an ideal gas in a cylinder with perfectly conducting walls fitted with a weightless, frictionless, and movable piston. A small amount of work done for a small change in volume dV at constant pressure is
    dW = P dV
Work done during isothermal processTherefore, when the gas expands from the initial state A (P1, V1) to the final state B (P2, V2), the total amount of work done is given by
Total work doneFor n-mole of gas, we have
    PV = nRT
    P = nRT/ V

Putting this value in equation (i)

Work doneFor isothermal process we know
    P = constant
    V = constant, then
    PV = constant
    P1V1 = P2V2
    P1/P2 = V2/V1
Then equation (iii) can also be written as,
    W = nRT logP1/P2 …….. (iv), Which gives the work done during the isothermal process.

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