Energy Analysis of Closed System

Moving Boundary Work:

The expansion  and compression work associated with a piston cylinder device in which boundary moves is called Moving Boundary Work.

Area under the Process curve on a PV Diagram:

From the above figure, the differential area is the product of pressure and differential volume. So the area under the Process curve is given by:

The area under the Process cure on a PV Diagram is Moving Boundary Work.

Moving Boundary Work in A constant Volume Process:

Moving boundary work is given by:

Moving Boundary Work for a Constant Pressure Process:

Moving Boundary Work is given by:

Moving Boundary Work for an Isothermal Process:

A thermodynamic process in which temperature remains constant durine the heat transfer is called Isothermal Process.

Moving Boundary Work is given by:

Where; 

 PV = mRT 

If temperature is constant,then 

PV = c 

P = c/V 

Moving Boundary Work for Polytropic Process:

During actual compression and expansion processes of gas, pressure and volume are related by P (V^n) = constant. Where n and c are constant. This process is called Polytropic Process.

Moving Boundary Work is given by:

Where;

PV = mRT 

Therefore;

Specific Heat:

It is defined as;

The Amount of heat energy requI red to raise the temperature of a unit mass of a substance by 1° C.

Difference Between Specific Heat at Constant volume and at Constant pressure:

Derivation of Cp and Cv:

The conservation of energy principle for a fixed mass, stationary closed system undergoing a Constant volume process in the differential form can be written as:

The left hand side of the above equation represents the net amount of energy transfer to the system from the definition of Cv, this energy must be equal to Cv dT.

Similarly, an expression for the specific heat at Constant pressure Cp can be obtained by considering a Constant Pressure Process.

Few observations can be made:

1) Cp and Cv are derived quantities.

2) Cv is related to the change in Internal Energy.

3) Cp is related to the change in Enthalpy.

The Enthalpy is also a function of temperature for an ideal gas.

h = u + PV 

h = u (T) + RT 

h = h (T) 

So, for an ideal gas the equation  (1) and (2) becomes 

The total change in Internal energy and enthalpy during a process from statemperature (1) to state (2) cam be determined by integration.

Methods to find Change in Internal Energy and Enthalpy:

a) Method-1: 

b) Method-2:

c) Method-3: 

Specific Heat Relations for an Ideal Gas:

Firstly, the Enthalpy is given by: