WORK AND HEAT
Positive work is done by a system, during a given process, when sole effect external to the system could be reduced to the lifting of a mass.
Units of Work and Power
In the international system (SI), unit is Joule.
In most of the applications large quantity of work is involved. Therefore kJ is commonly used.
Rate of doing work is known as power. Hence its unit is Nm/S or J/S which is again given a
special name Watts(W)
• Work and heat – are a Path Functions
Sign Convention of Work
Work done by the system on the surroundings is considered as positive work.
Work done on the system by the surroundings is taken as negative work.
Heat given into a system is positive
Heat coming out of the system is negative
Fig. Sign convention of work
Displacement work
Work done = pdV
where dV - change in volume.
This work is known as displacement work or pdV work corresponding to the elemental displacement dx. To obtain the total work done in a process, this elemental work must be added from the initial state to the final state. Mathematically
Constant Pressure Process
The mathematical expression for displacement work can be obtained as follows:
= p(V2 – V1)
This expression shows that the area under a curve in a p-V diagram gives work done in the process.
Constant volume process
Consider a gas contained in a rigid vessel being heated. Since there is no change in volume, the displacement work .
W=0
Isothermal Process (Hyperbolic process)
Let the product of pressure and volume remains constant at all the intermediate states of a process. In the p-V diagram it will be a hyperbola as given in Figure.
W = p1V1ln(V2/V1) = p2V2ln (V2/V1)
For Ideal gases when temperature remains constant, pV will be constant i.e., isothermal process are hyperbolic processes for an ideal gas.
Polytrophic Process
Any process can be represented by the general form pVn = constant. Based on the valve of n, the process differs as given below; for other values of n, the process is known as polytropic process. Figure. Shows the polytrophic process of various possible polytrophic indexes ‘n’ on p-V coordinates. Expression for displacements work for a polytropic process can be obtained as follows:
Adiabatic Process
Displacement work involved in a reversible adiabatic process can be expressed as
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