Adiabatic Expansion

Thermodynamics refers to the movement of heat energy between a system and its surroundings, and the conversion of heat into mechanical energy and vice versa.

Thermodynamic System 

A thermodynamic system is a collection of molecules or atoms contained within an area under a specific pressure (P), volume (V), and temperature (T), which are the fundamental properties of that system.

The term “surroundings” refers to everything outside of this system that exchanges heat or mass. Based on the interconnectedness of a system with its surroundings, thermodynamic systems are categorised into three groups:

(a) Open system: An open system is one in which both heat and mass are exchanged with the system’s environment or surroundings.

(b) Closed system: A system is considered closed if it only exchanges heat and no mass with its environment or surroundings.

(c) Isolated system: A system is considered isolated if there is no exchange of heat or mass with the environment or surroundings.

Laws of Thermodynamics

The laws of thermodynamics are as follows :-

Zeroth law of thermodynamics :

If two systems (B and C) are in thermal equilibrium with a third system (A), then B and C are said to be in thermal equilibrium with each other.

First law of thermodynamics :

The first law of thermodynamics is often known as the law of conservation of energy. It asserts that when a system absorbs heat dQ, the heat is converted into internal energy dU and work dW for the system. Then dQ = dU + dW

But, dW = PdV

Then, dQ = dU + PdV

which is the first law of thermodynamics mathematical equation.

When a system gains heat, both the work done by the system and the increase in its internal energy are considered positive.

On the other hand, when a system loses heat, the work done on it along with a decrease in its internal energy are deemed negative.

Second law of thermodynamics :

This law determines the direction in which heat moves.

According to Classius, it is impossible to design a machine that can transfer heat from an object lower in temperature to one that is comparatively higher, without the aid of an external source.

According to the Kelvin-Planck statement, there is no machine that can be developed that operates on a cyclic process, receives heat from a source, converts it into work, and rejects no heat to sink. To put it simply, no machine can perform 100% of the task.

Equation of State (for ideal gases) 

The equation of state is the relationship between the P,V,T of the thermodynamic system. PV = nRT is the equation of state for an ideal gas with n moles.

The parameters P, V, and T are also known as thermodynamic variables.

Work done by a gas 

The volume (V) and pressure (P) of the gas, and the piston’s area (A) are used to calculate the force applied on the piston by gas. The formula for calculating the same is F = PA.

Allow the piston to travel a modest distance dx during the gas expansion. 

dW = Fdx = PAdx is the work done for a little displacement dx.

Since A dx = dV, the increase in gas volume is dV.

⇒ dW = P dV

or W = ∫ dW = ∫ PdV

The work done during the process is represented by the area contained by the P-V curve.

Meaning of adiabatic expansion

If no heat is supplied to, or received from a system, it is said to be adiabatic. The temperature changes in this condition without adding any heat. In this type of process, the molar heat capacity is

Cadiabatic = △Q / n△T = zero

The gas’s internal energy decreases as a result of the work it does in this process. When a gas enclosed in a container with adiabatic walls expands, the system’s internal energy decreases, and the temperature drops. The temperature rises when the gas is compressed adiabatically.

The equation for the adiabatic process is:

PV𝜸 = constant   [Poission law]

T𝜸 P1 – 𝜸 = constant

T V𝜸 – 1 = constant

Slope of P-V curve in adiabatic expansion :

Since PV𝜸 = constant 

dp / dV = -𝜸(P / V)

Slope of P-T curve in adiabatic expansion :

Since T𝜸 P1 – 𝜸 = constant

dV / dT = – 𝜸P / (1-𝜸)T =  𝜸P / (𝜸-1)T 

Work done in adiabatic Process : 

△W = – △ U = nCv (Ti – Tf)

 = Pi Vi – Pi Vi / ( 𝜸-1) = nR(Ti – Tf ) / 𝜸-1

 The work done by a system is (+ve) if Ti > Tf (hence expansion takes place).

 The work done on a system is (- ve) if Ti < Tf (hence compression takes place).

Conclusion

Adiabatic expansion is the thermodynamic process in which the pressure decreases or the volume increases when the temperature is constant. Thermal equilibrium is maintained throughout the procedure. This article covers thermodynamic systems, several types of thermodynamic processes, and the specifics of isothermal expansion processes. Work performed during an isothermal expansion process is also covered.