Question

Derive an expression for work done in adiabatic process.

Answer 1

Hint:Think about a disconnected non-directing chamber, with a non-leading cylinder and afterward pull the cylinder just barely outward which will cause an adjustment in the states of being of the gas, and afterward discover the work done to roll out the improvement.

Complete step by step answer:
Assume we have a one-gram atom of an ideal gas which has been encased in a non-leading chamber having a non-directing cylinder. The gas will grow on the off chance that we move the cylinder gradually outwards and henceforth will accomplish some work with no energy being provided from outside and subsequently adiabatic extension will occur. What's more, since the energy hasn't been utilized from outside, the temperature of the gas in the chamber will fall.
Adiabatic cycle : $P{V^y} = K$
Along these lines, $P = K{V^{ - y}}$
Work done $W = \int {PdV} $
Or then again $W = \int {K{V^{ - y}}dV} $
Or on the other hand $W = \dfrac{K}{{1 - y \times [{V_2}^{ - y + 1} - {V_1}^{ - y + 1}]}}$
Or on the other hand $W = \dfrac{1}{{1 - y \times [{V_2}^{ - y + 1} - {V_1}^{ - y + 1}]}}$
Or then again $W = \dfrac{1}{{1 - y \times [{P_2}{V_2}^y{V_2}^{ - y + 1} - {P_1}{V_1}^y{V_1}^{ - y + 1}]}}$
Or on the other hand $W = \dfrac{{{P_2}{V_2} - {P_1}{V_1}}}{{1 - y}}$
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Note:
In thermodynamics, an adiabatic cycle is a sort of thermodynamic cycle which happens without moving warmth or mass between the framework and its environmental factors. In contrast to an isothermal cycle, an adiabatic cycle moves energy to the environmental factors just as work. It likewise thoughtfully bolsters the hypothesis used to clarify the main law of thermodynamics and is hence a key thermodynamic idea.
A cycle without movement of warmth or matter to or from a framework, so Q = 0, is called adiabatic, and such a framework is supposed to be adiabatically secluded. The supposition that a cycle is adiabatic is an as often as possible made disentangling presumption. The presumption of adiabatic seclusion is helpful and frequently joined with other such admirations to compute a decent first estimation of a framework's conduct.