Question

State first law of thermodynamics and derive mathematical expression for it

Answer 1

Explanation:

First law of Thermodynamics

If some quantity of heat is supplied to a system capable of doing external work, then the quantity of heat absorbed by the system is equal to the sum of the increase in the internal energy of the system and the external work done by the system.

Q=W+∆U

or

∆Q=∆U+∆W

• This law is applicable to every process in nature.
• The first law of thermodynamics introduces the concept of internal energy.
• The first law of thermodynamics is based on the law of conservation of energy.
• Q,∆U and W must be expressed in the same units (either in units of work or in units of heat ).
• This law is applicable to all the three phases of matter , i.e., solid , liquid and gas.
• U is a characteristics of the state of a system , it may be any type of internal energy - translational kinetic energy , vibrational , rotational kinetic energy , binding energy etc.

Answer 2

According to the first law of thermodynamics, during any transformation, there is conservation of energy.

In the case of closed thermodynamic systems, it is stated as follows:

"During any transformation of a closed system, the variation of its energy is equal to the quantity of energy exchanged with the external environment, by thermal transfer (heat) and mechanical transfer (labor). "

ΔQ = ΔU + W

where,

Q = Heat supplied to system

U = Increase in internal energy

W = Work done by system

The variation of the energy of a system which undergoes a transformation can be expressed according to the following relation:

ΔE = ΔU + ΔEc + ΔEp = W + Q

ΔE =  the sum of the different energy variations of the system.

ΔU = increase in internal energy

ΔEc = the variation of the macroscopic kinetic energy of the system

ΔEp =  the variation of the potential energy of the system

ΔW = Work done by system

ΔQ = Heat supplied to a system