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*Throttling Process:*

Throttling Process is the irreversible steady flow expansion process in which perfect gas is expanded through the orifice of minute dimensions like the narrow throat of the slightly opened valve. During procedure, fluid passes through the narrow opening (needle valve) from the region of constant high pressure to the region of constantly lower pressure adiabatically. Throttling is also called as Joule-Kelvin expansion.

Consider the cylinder which is thermally insulated and equipped with two non-conducting pistols on opposite sides of the porous wall. The left hand side of porous plug is filled with gas at P_{i} and V_{i} while right hand side is empty. Assume two pistons are moved simultaneously to right in such a way that constant pressure P_{i} is maintained on right hand side of wall while the constant lower pressure P_{f} is maintained on right hand side. After all gas has seeped through porous wall, final equilibrium state of system is achieved. This type of process is called as throttling process.

The throttling process is the irreversible process. This is due to gas passes through non-equilibrium states on its way from initial equilibrium state to final equilibrium state. As you know, non equilibriums states can't be explained by thermodynamic coordinates that is non-equilibrium states between initial and final equilibrium states during the throttling process can't be explained using thermodynamic coordinates.

**Enthalpy during throttling process:**

One of the most exciting properties of enthalpy function (H) is in connection with throttling process. Equation of first law of thermodynamics is

dQ = dU - w

but throttling process occurs adiabatically,

dQ = 0 (adiabatic process)

Then, the first law of thermodynamics becomes

dU = W

and work

W = -∫_{0}^{Vf} PfdV - ∫_{vi}^{0}PidV

Since both pressures ( P_{i} and P_{f} ) remain constant, equation becomes

W = - (P_{f}V_{f} - P_{i}V_{i})

Rearranging provides

U_{i} - P_{i}V_{i} =U_{f }- P_{f}V_{f}

But enthalpy H = U - PV, so equation becomes

H_{i} = H_{f}

In the throttling process, thus, initial and final enthalpies are equal.

Throttling process is very helpful in refrigeration. The continuous throttling process can be attained using apparatus.

**Free Expansion of a Gas:**

Concept of work done by or on the system has been treated under first law of thermodynamics. Work done by or on the gas in the cylinder with the moveable piston was derived to be

dW = -PdV

Above equation is due to expansion or compression of the gas in the cylinder. That is, in the case of expansion, molecules move faster and push piston (applied the force on piston) and move piston through distance.

Now consider, for instance, the composite system comprising of the hydrostatic fluid in compartments 1 and 2 with (P_{1}, V_{2}) and (P_{2}, V_{2}) respectively.

Each compartment or both compartments can go through adiabatic work by interacting with surroundings. This may be done by moving one or both pistons in or out, either slowly (a quasi-static process) so that work done W = -∫ PdV , with pressure P being equal to equilibrium value (i.e. for the quasi-static process system is in equilibrium at every instant). In addition piston can be moved very rapidly (the non-quasi-static process) so that pressure at the face is less that equilibrium value. For these two examples, work is done on piston because of expansion of fluid. Though, if either or both of pistons is or are pulled out at the faster rate than velocity of molecules of fluid, fluid will perform no work on piston at all. This kind of process is known as the free expansion of a gas. Assume system is thermally insulated and that compartment 1 has a gas while other compartment is empty. If partition is removed, gas will go through what is called as free expansion in which no work is performed and no heat is transferred. From first law of thermodynamics, as both Q and W are zero, it follows that internal energy remains unchanged during the free expansion. For free expansion of gas, work is zero (W = 0) and no heat is transfer (Q = 0). Equation of first law of thermodynamic reduces to

dU = 0

**Temperature Change during Free Expansion:**

The value of temperature change (∂T/∂V)U during free expansion process has employed attention of physicists for over 100 years. Joule and many others tried to estimate either the quantity (∂T/∂V)U, that may be known as Joule Coefficient, or related quantities that are all a measure of effect of the free expansion-often known as Joule effect. Results of their experiments illustrated that (∂T/∂V)U = 0 for ideal gas, but not for real gas.

**Internal Energy U during Free Expansion:**

Internal energy U of gas, like any state function, is the function of any two of coordinates P, V, and T. Now consider U as the function of T and V i.e. U(T, V), then derivative of U is

dU = (∂U/∂T)VdT + (∂U/∂V)TdV

If temperature change is equal to zero (i.e. dT = 0), and for free expansion (dU = 0 ), then equation becomes

(∂U/∂V)T = 0

This means that U doesn't depend on V.

Also consider U as the function of T and P i.e. U(T, P), derivative of U is

dU = (∂U/∂T)PdT + (∂U/∂P)TdP

If temperature change is equal to zero (i.e. dT = 0) and for free expansion (dU = 0), then equation becomes

(∂U/∂P)T = 0

This Equation means that U doesn't depend on P. These equations follows that if no temperature change takes place in the free expansion process, U is independent of V and P, and thus U is the function of T only.

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