This law is the simplest and one of the most important statements of Thermodynamics.
It says: “Energy can neither be created nor destroyed.”

That is energy of the universe remains constant or conserved. Let’s study application of this law on our standard system of a gas. We know that internal energy of this system can changed by heat and work. But all the changes will be finally reflected in the internal energy of the system. For example, if work increases the internal energy by 100 J and at the same time heat decreases the internal energy by 100 J then the net change in internal energy will be zero. Therefore we can say that change in internal energy is the sum of heat and work.
U = q + w
This is the mathematical statement of First law. Here the signs of q and w become very significant. For this we have proper sign conventions to be used.
Sign Conventions for First law
We will use very simple and straight forward sign convention. Any change that tends to increase the internal energy of the system is taken as positive and any change which tends to decrease the internal energy is negative. That is, heat supplied to the system and work done on the system by the surroundings are both positive and vice versa.
For example, if 200 J work is done on the system by pushing the piston inside and 100 J heat is withdrawn from the system then:
U = q + w = – 100 + 200 = + 100 J
Internal energy will increase by 100 J in the process.
“Any energy given to the system is positive and any energy withdrawn from the system is negative.”
The sign convention in thermodynamics: w and q are positive if energy enters the system (as work and heat, respectively), but negative if energy leaves the system.
Sign convention for work done can be best remembered by observing the volume change.
If volume of the system decreases positive work is done on the system and if volume increases then negative work is done.

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