Derivation for workdone in isothermal process?

Answer 1

In thermodynamics, an adiabatic process or an isocaloric process is a process in which no heat is transferred to or from working fluid. The term "adiabatic" literally means an absence of heat transfer; for example, an adiabatic boundary is a boundary that is impermeable to heat transfer and the system is said to be adiabatically (or thermally) insulated. An insulated wall approximates an adiabatic boundary. Another example is the adiabatic flame temperature, which is the temperature that would be achieved by a flame in the absence of heat loss to the surroundings. An adiabatic process which is also reversible is called an isotropic process.

Ideal gas:

For a simple substance, during an adiabatic process in which the volume increases, the internal energy of the working substance must necessarily decrease. The mathematical equation for an ideal fluid undergoing an adiabatic process is,

p.v^( γ )

where P is pressure, V is volume, and

γ =CP/CV=α +1 / α .

CP being the molar specific heat for constant pressure and CV being the molar specific heat for constant volume. α comes from the number of degrees of freedom divided by 2 (3/2 for monotonic gas, 5/2 for diatomic gas). For a monotonic ideal gas, γ = 5 / 3, and for a diatomic gas (such as nitrogen and oxygen, the main components of air) γ = 7 / 5. Note that the above formula is only applicable to classical ideal gases and not Bose-Einstein or Fermi gases.

For the derivation of work done in an adiabatic process, please visit the link I added below.