## Isothermal Process

### Isothermal Process

1. An isothermal process is one in which the pressure and volume of the system change but temperature remains constant.
2. An isothermal process may be achieved
a) If the gas is enclosed in a vessel whose walls are made of highly conducting material and
b) The gas is compressed or allowed to expand very slowly.
3. When the gas expands, cooling will take place. But because the gas expends very slowly; hence before the temperature of the gas falls, heat is conducted into the cylinder through the conducting walls from the surroundings i.e., temperature of the gas remains almost constant. On the other hand, when the gas is compressed slowly, the heat produces escape to surroundings through the conducting walls before it could increase the temperature og the gas i.e, temperature of the gas again remains almost constant.
4. In case of ideal gas, the internal energy remains constant in isothermal process because internal energy of an ideal gas depends on temperature only.
5. Because dU =0 in this process, hence in accordance to first law of thermodynamics, the amount of heat supplied is equal to the work done by the gas.
6. As the change in temperature is zero, hence the molar heat capacity in such process is
Cisothermal = ΔQ/μΔT = infinity
7. For one mole of an ideal gas, PV=RT.
As temperature remains constant in an isothermal process, hence PV = constant
Above equation (called as Boyle’s law) represents the equation of an isothermal process for an ideal gas.
8. First law of thermodynamics applied to isothermal process:
Internal energy of an ideal gas depends on the temperature only. Because temperature remains constant in an isothermal process, hence there is no change in internal energy in this process i.e., dU = 0. Therefore, according to first law of thermodynamics,
dQ = dU +dW or
dQ=dW
a) In this process of isothermal expansion, as work is done by the system, hence dW is positive. Consequently dQ will also be positive. Therefore, if a gas is to expand isothermally, then an amount of heat equivalent to work done by the gas will have to be supplied to it from the external source.
b) In the process of isothermal compression, as work is done by the system, hence dW is positive. Consequently dQ will also be negative.
Therefore, if a gas is to compress isothermally, then an amount of heat equivalent to work done by the gas will have to be removed from it.
c) When a gas undergoes isothermal expansion or compression, ther is no change in the internal energy of the gas.