The ideal gas equation states PV=nRT
but this is not applicable for real gas because for ideal gas volume of the gas is considered negligible as compared to volume of the container.
Similarly the intermolecular force of attraction is compared negligible
In case of real gas volume of gas is not negligible so volume is reduceded and pressure is increased due to increase in intermolecular force of attraction
the vanderwall gas equation
(P+ansquare/vsquare)(V-nb)=nRT

Wander-Vaal's Equation:

The Wander-Vaal's equation is a mathematical relationship that describes the behavior of a semiconductor device known as a bipolar junction transistor (BJT). This equation is named after two scientists, John R. Wander and Jan H. Vaal, who derived it in 1956. The Wander-Vaal's equation provides a model for the current-voltage characteristics of a BJT.

The Equation:
The Wander-Vaal's equation can be expressed as:

Ic = Ic0 * (e^(Vbe/Vt) - 1)

Where:
- Ic is the collector current
- Ic0 is the reverse saturation current
- Vbe is the base-emitter voltage
- Vt is the thermal voltage (k * T / q, where k is Boltzmann's constant, T is temperature in Kelvin, and q is the charge of an electron)

Explanation:
The Wander-Vaal's equation is derived from the basic principles of semiconductor physics and the behavior of a BJT. Let's break down the components of the equation and understand their significance:

1. Collector Current (Ic):
- The collector current represents the flow of current between the collector and emitter terminals of the transistor.
- It depends on the base-emitter voltage and the reverse saturation current.

2. Reverse Saturation Current (Ic0):
- The reverse saturation current is the current that flows when the base-emitter junction is in reverse bias.
- It represents the leakage current in the transistor when there is no forward bias applied.

3. Base-Emitter Voltage (Vbe):
- The base-emitter voltage is the voltage across the base-emitter junction.
- It controls the current flow in the transistor and affects its behavior.

4. Thermal Voltage (Vt):
- The thermal voltage represents the thermal energy of the semiconductor material.
- It is proportional to the temperature and affects the behavior of carriers in the transistor.

Significance:
The Wander-Vaal's equation is significant in transistor modeling and circuit analysis. It helps engineers and researchers understand and predict the behavior of BJTs under different operating conditions. By knowing the values of Ic0, Vbe, and Vt, one can calculate the collector current accurately using this equation.

Conclusion:
The Wander-Vaal's equation is a fundamental equation in the study of bipolar junction transistors. It provides a mathematical model to describe the current-voltage characteristics of a BJT. Understanding this equation is crucial for designing and analyzing transistor circuits in various electronic applications.