First Law of Thermodynamic

The First Law of Thermodynamics is a fundamental principle of energy conservation applied to thermodynamic systems. It states that energy can neither be created nor destroyed; it can only be transformed from one form to another. This law establishes the relationship between heat, work, and the internal energy of a system.

In simple terms, when heat is supplied to a system, that energy is either:

• Stored in the system as internal energy, or

• Used by the system to do work on its surroundings.

Statement of the First Law

The increase in internal energy of a system is equal to the heat supplied to the system minus the work done by the system on its surroundings.

Mathematical Expression

For a closed system:
\delta Q = dU + \delta W

Where:

• ( \delta Q ) = Heat supplied to the system

• ( dU ) = Change in internal energy

• ( \delta W ) = Work done by the system

For finite changes:
Q = \Delta U + W

Terms Explained

1. Heat (Q)

Energy transferred due to temperature difference between system and surroundings.

2. Work (W)

Energy transfer when a force causes displacement (e.g., piston movement in a cylinder).

3. Internal Energy (U)

The total microscopic energy stored within a system due to molecular motion and interactions.

First Law for Different Processes

1. Constant Volume Process (Isochoric)

• No work done: ( W = 0 )

• Q = \Delta U

2. Constant Pressure Process (Isobaric)

• Work done: ( W = P \Delta V )

• Q = \Delta U + P \Delta V
  

3. Isothermal Process (Constant Temperature for ideal gas)

• ( \Delta U = 0 )

• Q = W

4. Adiabatic Process

• No heat transfer: ( Q = 0 )

• \Delta U = -W

First Law for a Cyclic Process

In a thermodynamic cycle:

[
\Delta U = 0 \Rightarrow Q = W
]

Net heat supplied equals net work done.

First Law for an Open System (Control Volume)

For steady-flow systems like turbines, compressors, boilers:

Q - W = \Delta H + \Delta KE + \Delta PE

Where:

• ( H ) = Enthalpy

• ( KE ) = Kinetic energy

• ( PE ) = Potential energy

Practical Applications

• Internal combustion engines

• Steam turbines and boilers

• Refrigeration and air conditioning

• Compressors and pumps

• Power plants and heat exchangers

Limitations of the First Law

• Does not indicate the direction of heat flow

• Does not explain why heat flows from hot to cold

• Cannot predict feasibility of processes

• Does not account for entropy

These are addressed by the Second Law of Thermodynamics.

Example

If 500 kJ of heat is supplied to a gas and the gas does 200 kJ of work:
\Delta U = Q - W = 500 - 200 = 300 \text{ kJ}

The internal energy increases by 300 kJ.