Relation between work and heat

Relation between work and heat

Introduction : In our day to day life such as boiling water, hot cup of tea , hot cup of water, etc we come across important term physical quantity such as heat, work, internal energy. In this topic we are going to see more about first law of thermodynamics.

Consider an illustrative example

Case I : From the figure A below, a thermodynamic model consist of a gas (system) in a container attached with a movable, frictionless piston. When the gas expands, the piston is moved outward and the work is done by gas on the piston. Thus the gas does a positive work (+W).  System looses it's energy in the form of heat. Heat is lost by system thus heat is negative (-ve). 

Figure A

Case II : From the figure B below, a thermodynamic model consist of a gas (system) in a container attached with a movable, frictionless piston. When the gas is compressed, the piston  moves inward and the work is done on the gas by the piston. Thus the surrounding does a negative work (-W). System gains  energy in the form of heat. Heat is lost by surrounding thus heat is positive (+ve). 

Figure B

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Work done 

From the figure C above, let system does the work in pushing piston outward.

Let the piston is moved by a infinitesimal small distance  dx. 

Thus work done by piston is given by,

 dW = F . ds-----(1)

The force exerted by system on piston is given by  

F = PA------(2)

from (1) and (2)

dW = P A ds  ---(3)

We know ( A.ds = dV)

Thus Equ (3) changes to

dW = PdV   

If initial volume is V_i and final volume of gas after expansion is V_f . then the total work done is given by,

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