Isothermal process Totally Explained

Everything about Isothermal totally explained

An isothermal process is a thermodynamic process in which the temperature of the system stays constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and processes occur slowly enough to allow the system to continually adjust to the temperature of the reservoir through heat exchange. An alternative special case in which a system exchanges no heat with its surroundings (Q = 0) is called an adiabatic process. Consider an ideal gas, in which the temperature depends only on the internal energy, which is a function of the mean translational kinetic energy of the molecules, as given by a Boltzmann distribution; if the internal energy is constant, so is the temperature. Take the number of moles n as a constant. ť

Delta U = n R Delta T = 0 ,

but this means, according to the ideal gas law, that ť

Delta (P V) = 0 ,

so that ť

P_i V_i = P V = P_f V_f ,

where

P_i

and

V_i

are the pressure and volume of the initial state,

P_f

and

V_f

are the pressure and volume of the final state, and the variables P and V stand for the pressure and volume of any intermediate state during an isothermal process.
Curves called isotherms appear as a hyperbolas on a P-V (pressure-volume) diagram (T = constant). Each one asymptotically approaches both the V (abscissa) and P (ordinate) axes. This corresponds to a one-parameter family of curves, a function of T, whose equation is ť

P =

Isothermal processes can occur in any kind of system, including highly structured machines, and even living cells. Various parts of the cycle of some heat engines are carried out isothermally and may be approximated by a Carnot cycle.

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