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Equation for Conservation of Mass

To apply the first law of thermodynamics, we reduce the situation to a fixed or control mass problem. A general representation of an open system is shown in Fig. 5.2 where the working substance in the control volume at time ‘t has mass m’t and energy E ‘t. And at time interval of crt, mass dmin at state 1 enters the control volume, and mass, d mout at state 2 leaves the control volume. In addition heat supplied to the control volume is dQ and amount of work transfer is net· As a result the mass at t  and energy is Et + t·

 

we can write down 1-1 =>  IN section

2-2 => OUT section

Initial mass = mt + δmin

Final mass = mt + δt

So mass balance is given by

Dividing by δt,and takingd1  we obtain