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.
Application 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
Therefore, 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
For n-mole of gas, we have PV = nRT
P = nRT/ V
Putting this value in equation (i)
For 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 loge P1/P2 …….. (iv), Which gives the work done during the isothermal process.
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