Thermodynamic process of perfect gases

Thermodynamic process of perfect gases:-

This process of heating or cooling of a gas is defined as a thermodynamics process. It has been observed that during a thermodynamic process take place in various properties of the gas chest pressure, volume, temperature, specific energy, specific enthalpy etc. Following thermodynamics process are important..

 constant volume process for isochoric process:-

when the gas is heated at a constant volume its temperature and pressure will increase. Since there is no change in 8th volume no external work is done by the gas. All the heat supplied is stated in the body of the gas in the form of internal energy. It may be noted that this process is governed by gay lussac law.
Now consider m kg of a certain being heated at constant volume from an initial temperature T1 to final temperature T2. This process is p-v diagram slope.

** it may be noted that the area below the p-v diagram of a thermodynamic process represents the work done during the process to some scale.

we know that, Q1-2 = (U2 – U1) + W1-2 =U1 – U2
We also know that the internal energy,
U1 – U2 = m.cv (T2 – T1)
Heat supplied, Q1-2 = (U1-U2) = mcv (T2-T1)

 

constant pressure process or isobaric process:-

when the gas is heated at constant pressure at temperature at volume will increase. Since there is a change in volume the heat supplied is utilised in increasing the internal energy of the gas and also for doing some external work. It may be noted that this process is governed by Charles law.

Now consider m kg of a certain gas being heated at constant pressure from an initial temperature T1 to final temperature T2. This process is shown on the p-v diagram.
We know that heat supplied to the gas at constant pressure,
Q1-2 = m.cp (T2 – T1)
Increase in internal energy,
U2 – U1 = m.cv (T2 – T1)
And work done during the process or the gas,
W1-2 = Area below the line 1-2
= p(v2-v1) = m.R(T2 – T1)

Hyperbolic process:-

a process in which the gas is heated or expanded in such a way product of pressure and volume remain constant is called a hyperbole process. This process is governed by Boyle’s law, pv= constant. If we plot a graph for pressure and volume during the process we get a rectangular hyperbola and hence this process is known as hi parabolic process. Its practical application is isothermal process as discuss….

Constant temperature process for isothermal process:-

a process in which the temperature of the working substance remains constant during it expansion or compression is called a constant temperature process for isothermal process. This will happen when the working substance remains in a perfect thermal contact with the surrounding so, get the heat sucked in or squeezed out is compensated exactly for the mechanical work done by or on the gas respectively. It is dance obvious that in an isothermal process.

1) there is no change in temperature.
2) there is no change in internal energy

We know that, Q1-2 = dU + W1-2 = W1-2
Hence during isothermal expansion of a gas,
Heat added = Work done by the gas,
Similarly, during isothermal compression of a gas,
Heat subtracted = Work done on the gas

A little consideration will show that the isothermal process is governed by Boyle’s law. Does the isothermal equation of a perfect gas is pv = constant.
v1= initial volume of gas.
p1= initial pressure of gas.
v2= final volume of gas
p2= final pressure of gas.
The workdone during isothermal expansion is given by,

W1-2 = Area under the curve 1-2
= p1v1 loge (v2/v1) = 2.3 p1v1 log (v2/v1)
= 2.3 mRT log (v2/v1) = 2.3 mRT log (p1/p2)
In general, W = 2.3 p1v1 log r = 2.3 mRT log r [ r is the compression ratio]

Adiabatic process or Isentropic process:-

a process in which the working substance neither receive nor gives out to its surrounding during it function or compression is called an adiabatic process. This will happen when the working substance remained thermally insulated so that no heat enters or leaves eat during the process. It is thus obvious that in an adiabatic process.

1) no heat leaves or enter the gas.
2) the temperature of the gas changes as the work is done at the cost of internal energy.
3) change in internal energy is equal to the work done.

We know that, Q1-2 = dU + W1-2 or dU = – W1-2

(Minus sign indicates that for increase in internal energy work must be done on the gas(i.e -ve work must be done by the gas). Similarly please in internal energy work must be done by the gas).

** a frictionless activity process is known as isentropic process or constant entropy process.

Now considered a certain quantity of a perfect gas being expanded adiabatically which is shown by the curve

Let,.
v1= initial volume of gas
p1= initial pressure of gas
v2= final volume of gas
p2= final pressure of gas

The work done during adiabatic process is given

W = p1v1 – p2v2 / ᵞ-1 = mR (T1 – T2) / ᵞ – 1
= p2v2 p1v1 / ᵞ – 1 = mR (T2 – T1) / ᵞ – 1

**Notes-
a) for adiabatic process, p1v1ᵞ = p2v2ᵞ = constant, { ᵞ is adiabatic index}

b) since p1v1 = mRT1 and p2v2 = mRT2 therefore the above the equation my be written as,…
T1 / T2 = (v1/v2) ᵞ-1 = (p1 / p2) ᵞ-1

Polytropic process:-

the polytropic process is also known as the general law for the expansion and compression of gas and is given by the relation
pvn = constant.

Where n is a polytropic index may have any value from zero to infinity, depending upon the manner in which the expansion or compression has taken place. Radius equation for polytropic process may be expressed by the change the index n for in the adiabatic process.

The heat absorbed or rejected during the polytropic process(i.e. pvn = constant) is given by

Q = ᵞ -n / ᵞ – 1 x workdone = ᵞ – n / ᵞ -1 x p1v1 – p2v2 / n – 1
= ᵞ – n / ᵞ – 1 x mR(T1 – T2) / n – 1 = ᵞ – n / ᵞ – 1 x m.cv (T1 – T2)

Free expansion( or unresisted expansion) process:- free expansion occurs when a fluid is allowed to expand suddenly into a vacuum chamber through and orifice of large dimension. Hindi process no heat is supplied or rejected and no external work is done. Hence the total heat of the fluid remains constant. The type of expansion may also be called as constant total heat expansion. It is thus obvious, that in a free expansion process.

Q1-2 = 0, W1-2 = 0, and dU = 0

Throttling process:-

a perfect gas is expanded through an aperture of minute dimension, such as a narrow throat or slightly open bulb, dippo the process is termed as throttling process. During this process no heat is supplied aur rejected and also no external work is done, moreover there is no change in temperature and show the total heat of the fluid remains constant.

During the third link process the expansion of a perfect gas is under constant total heat condition, and resemble with free expansion process. Thought learning process,
Q1-2 = 0, W1-2 = 0, and dU = 0

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