How To Derive Equation Of Heat Transfer By Using First Law Of Thermodynamics And Analysis Of First Law Of Thrmodynamics

Thermodynamics has four laws zeroth law, first law, second law and third law. These are fundamental laws of thermodynamics. Till now no system or machine can abound them. These laws are actually nature’s law. They are a presence in life since the creation of time. They can be applied universally in our entire universe. Now here we are going to discuss first the law of thermodynamics from which energy conservation law was derived.

FIRST LAW OF THERMODYNAMICS:

State of this law is like this “for a cyclic process of any system summation of all heat transfers (no matter negative or positive) equals to a summation of all the work transfer.” 

It can be represented as ƩQ=ƩW. Before the establishment of this law, the scientist had tried to make a machine which could give output without any given input. This attempt was failed. This type of device is known as PMM 1 (perpetual motion machine first) which are impossible to make.

Now consider two reversible cycles as shown in a figure. (here A, B& C represent different paths).

1)       For cyclic process 1-A-2-B-1. Applying first law of thermodynamics

Now heat transfer and work transfer during 1-A-2 are expressed as Q_1-A-2 & W_1-A-2.

And for process 2-B-1, Q_2-B-1 & W_2-B-1.

Now according to the first law, we can write:

Q_1-A-2 +Q_2-B-1 =W_1-A-2+ W_2-B-1

2)      For cyclic process 1-A-2-C-1. Applying first law of thermodynamics

Now heat transfer and work transfer during 1-A-2 are expressed as Q_1-A-2 & W_1-A-2.

And for process 2-C-1, Q_2-C-1 & W_2-C-1.

Now according to the first law, we can write:

Q_1-A-2 +Q_2-C-1 =W_1-A-2+ W_2-C-1

·         

Now subtract first equation from second equation:

So we will get,    Q_2-C-1 -Q_2-B-1 =W_2-C-1 -W_2-B-1                       

_Þ  Q_2-C-1 -W_2-C-1  =   Q_2-B-1 -W_2-B-1  =   Q_2-M-1-W_2-N-1  ( here M and N represent some paths).

·         So from above equation, we can say that difference between n heat transfer and work transfer between two states (1 & 2) always remains same. It doesn’t change with a change of path. So this quantity is not way function but point function. This point function is known as ENERGY (E) of the system.

So for any single process,

                      Q-W=U Þ Q=W+E

But E = kinematic energy+ potential energy+ internal energy

Now here values of kinematic and potential energies are very small so neglect them

So E = INTERNAL ENERGY = U

SO ABOVE EQUATION CAN BE REWRITTEN AS

Q = W+U

dQ = dW + dU (if u take differential )

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