**Zeroth law:**If two bodies A and B are in thermal equilibrium and A and C are also in thermal equilibrium then B and C are also in thermal equilibrium.

**First law of thermodynamics**

∆U = ∆Q -∆W

Where

∆U = change in internal energy of a thermodynamic system

∆Q = Heat given to the system

∆W = work done by the system

Change in internal energy of a thermodynamic system is equal to the heat given to the system minus the work done by the system on surroundings or environment.

**Second law of thermodynamics**

Kelvin-Planck statement

It is not possible to design a heat engine which works in cyclic process and whose only result is to take heat from a body at a single temperature and convert it completely into mechanical work.

(Topic: Laws of Thermodynamics)

**1. Law of conservation of mass**

During any physical or chemical change, the total mass of the products is equal to the total mass of reactants.

**2. Law of constant proportions**

A pure chemical compound always contains same elements combined together in the same definite proportion by weight.

**3. Law of multiple proportions**

When two elements combine to form two or more than two compounds, the weights of one of the elements which combine with a fixed weight of the other, bear a simple whole number ratio.

**4. Law of reciprocal proportions**

When two different elements combine separately with the same weight of a third element, the ratio in which they do so will be the same or some simple multiple of the ratio in which they combine with each other.

**5. Gay Lussac’s law of combing volumes**

Under similar conditions of temperature and pressure, whenever gases react together, the volumes of the reacting gases as well as products (if gases) bear a simple whole number ratio.

**Lagrange's Identity**

(

**a**×

**b**)² = a²b² - (

**a**.

**b**)

**a**and

**b**are vectors

a and b are magnitudes of

**a**and

**b**respectively.

Lagrange's identity is a relation between the cross product and the dot product.

(Topic: Vectors)

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