Suppose a tank filled with gas is discharing, then the pressure and temperature will decrease.
consider two instances (p1,v1) and (p2,v2) with some time interval. If there is no heat addition then p2v1 the we will get some value for polytropic index. But if we heat the tank in such away that p2=p1, then how polytropic index can be calculated?
Whether this means that polytropic process relation cant be applied when there is external heat transfer.
If we consider a vertical cylinder with an internal gas, with a free pinton in the top end. Heat is supplied to the cylinder the process is to constant pressure. Since there is fulfilled that p.V^n=constant being n polytropic index. When the process is to constant pressure n it is equal to zero in order that it expires p.V^n=constan.
If we consider a vertical cylinder with an internal gas, with a free pinton in the in the free side. Heat is supplied to the cylinder the process is to constant pressure. Since there is fulfilled that p.V^n=constant being n polytropic index. When the process is to constant pressure n it is equal to zero in order that it expires p.V^n=constan.
Suppose ther is some liquid in tank which is expelled with the pressurized gas, then how can total volume expelled be calculated considering above scenario of pressure equalization between two time instances?
To apply the conservation of the mass to the whole volume in an instant t and then the conservation of energy to the liquid in this instant t. Then it joins between two considered conditions and decides to solution looked
To complement. It is necessary to to relate what happens in a system with regard to the volume of control. It is known as Reynolds's theorem.
According to the general definition, polytropics are REVERSIBLE (and not necessarily ADIABATIC) transformations of a gas in which pressure and specific volume are tied by the relationship: pv^n= const. If the gas happens to be an ideal gas, also the relationships: Tp^((1-n)/n) and Tv^(n-1) hold good. As far as the evaluation of n is concerned, one only needs to know initial and final states to compute the index from the relationship: p_1v_1^n=p_2v_2^n where n is the only unknown. In the particular case of p_1=p_2 one, obviously, obtains: n=0. See, for example: G. Comini and S. Savino, Themodynamic Fundamentals of Energy (unfortunately in Italian), SGE, Padua, 2011.
Actually, a polytropic process is usually not possible without external heat transfer. The only exception is when n=k or an isentropic process.
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