**Adiabatic process**

**Polytropic process**

**Constant Volume Process**

**Throttling Process**

The free expansion process is an irreversible non-flow process. A free expansion process occurs when a fluid is allowed to expand suddenly into a vacuum chamber through an orifice of large dimensions.

Consider two chamber A and B separated by a partition. Since there is no expansion of the boundary of the system, because it is rigid, therefore no work is done. Thus, for a free expansion,

**Q1-2 = 0; W1-2 = 0 and dU = 0**

The following points may be noted regarding the free expansion of a gas:

**1**. Since the system is perfectly insulated so that no heat transfer takes place therefore the expansion of gas may be called as an adiabatic expansion.

**2**. Since the free expansion of the gas from the equilibrium state 1 to the equilibrium state 2 takes place therefore the intermediate state will not be in equilibrium states.

etc...

Consider two chamber A and B separated by a partition. Since there is no expansion of the boundary of the system, because it is rigid, therefore no work is done. Thus, for a free expansion,

The following points may be noted regarding the free expansion of a gas:

etc...

Heat transfer during a polytropic process

Q1-2 = (segma) - n / (segma) - 1 * W1-2

where W1-2 is the work done during polytropic process.

If dQ is the small quantity of heat transfer during small change of pressure and volume, then

dQ = (segma) - n / (segma) - 1 * pdv

Rate of heat transfer per unit volume,

dQ / dv = (segma) - n / (segma) - 1 * p

Q1-2 = (segma) - n / (segma) - 1 * W1-2

where W1-2 is the work done during polytropic process.

If dQ is the small quantity of heat transfer during small change of pressure and volume, then

dQ = (segma) - n / (segma) - 1 * pdv

Rate of heat transfer per unit volume,

dQ / dv = (segma) - n / (segma) - 1 * p

and rate of heat transfer per second,

dQ / dt = dQ / dv * dv / dt = (segma) - n / (segma) -1 * p * dv / dt

where dv / dt is the swept volume of the piston per second.
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Rate of Heat Transfer

A process, in which the tempreture of the working substance remains constant during its expansion or compression, is called constant tempreture process or isothermal process. This will happen when the working substance remains in a perfect thermal contact with the surroundings, so th

at the heat "sucked in' or 'squeezed out' is compensated exactly for the work done by the gas or on the gas respectively. It is thus obvious that in an isothermal process:1. there is no change in tempreture.

2. there is no change in internal energy, and

3. there is no change in enthalpy.

Now consider m kg of a certain gas being heated at constant tempreture from an intial state 1 to final state 2.

Let p1v1 and T1 = Pressure, volume and tempreture at the intial state 1, and

p2v2 and T2 = Pressure, volume and tempreture at the final state 2.

A process, in which the gas is heated or expanded in such a way that the product of its pressure and volume (i.e *v ) remains constant, is called a hyperbolic process.

It may be noted that the hyperbolic process is governed by Boyle,s law i.e p v = constant. If we plot a graph for pressure and volume, during the process as shown in fig we shall get a rectangular hyperbola. Hence, this process is terned as hyperbolic process. It is merely a theoretical case, and has a little importance from the subject point of view. Its practical application is isothermal process, which is discussed below.

It may be noted that the hyperbolic process is governed by Boyle,s law i.e p v = constant. If we plot a graph for pressure and volume, during the process as shown in fig we shall get a rectangular hyperbola. Hence, this process is terned as hyperbolic process. It is merely a theoretical case, and has a little importance from the subject point of view. Its practical application is isothermal process, which is discussed below.

Labels:
Hyperbolic Process

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