What is  first law of thermodynamics .

First law of thermodynamics

The first law of thermodynamics states that the energy of an isolated system is constant.

ΔU = q + W, is the mathematical statement of the first law of thermodynamics.

where ΔU is the change in the internal energy of the system, q is the heat transferred and W is the work done. It basically means that energy can neither be created nor be destroyed, although it can be converted from one form to another. The first law of thermodynamics is actually an expression of the principle of conservation of energy .

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first law of thermodynamics states that internal energy is equal to heat transfers +  the work done

U  =  Q  +  W

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FIRST LAW OF THERMODYNAMICS STATES THAT INTERNAL ENERGY IS EQUAL TO HEAT TRANSFERS + WORK DONE

U=Q + W

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The First Law of thermodynamics basically says that energy or matter can neither be created nor destroyed. In terms of the machine, this meant that the total energy output (work by the machine) is equal to the heat supplied. First law of thermodynamics states that “the energy of an isolated system is constant”.

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The first law of thermodynamics is an expression of the principle of conservation of energy . It states that the energy can be transformed from one form to another, but cannot be created or destroyed. This law defines the internal energy (E) as equal to the difference of the heat transfer (Q) into a system and the work (W) done by the system. Mathematically, it is expressed as

All the Best

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First let me state the first law of thermodynamics for you.
It states that energy can neither be created nor can it be destroyed but it can be transformed from one form to another.
In other words, the total energy of the universe, i.e., system and surroundings remains constant during any physical or chemical process.
 
Here, is a very simplified and step-by-step method of deriving this law mathematically.
 
Let us assume that a system having internal energy U 1 absorbs a certain amount of energy q.
So, the internal energy becomes q + U 1.
If w is the amount of work done on it, then the internal energy changes to U 2.
 
Now, final internal energy (U 2) becomes U 1+ q+ w
So, U 2 = U 1+ q+ w
Or, U 2 - U 1 = q+ w
Or, ∆U= q+ w
So, in the above manner the first law of thermodynamics can be derived mathematically.

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