Question

How would you prove the first law of thermodynamics?

Answer 1

We know that thermodynamics is the study of the relationship between heat, work and temperature. These relationships follow the four laws of thermodynamics. The first law of thermodynamics roughly states that energy can be transferred from one system to another either as heat or work.
Formula used:
$\Delta U=Q-W$

Complete step by step answer:
Thermodynamics is the study of the interactions between the system and the surrounding. These interactions are mostly either by the transfer of heat or by the work done on by the system. These help in understanding the system by related properties like equilibrium and spontaneity.
Thermodynamics is governed by four laws, namely the zero-th, first, second and third law.
The first law of thermodynamics states that the total energy of an isolated system is constant. This is to say that the energy can neither be created nor be destroyed but it can only be transformed from one form to another.
The first law is mathematically written as
$\Delta U=Q-W$
Where, $\Delta U$ is the change in the internal energy, $Q$ is the heat energy supplied and $W$ is the work done by the system, assuming that the system here is closed.
Consider a system to have an internal energy $U_1$ when and external heat energy $Q$ is supplied to the system , the internal energy of the system increases to $U_2$.
This difference in internal energy is accounted for as the work done $W$ by the system.

Note: A closed system is a thermodynamic state where there is no exchange of heat or mass between the boundaries of the system and the surrounding. A closed system is also called the combination of adiabatic and rigid system as there is no loss in heat or matter from the system.