Question

What is first law of thermodynamics? With its help define internal energy.

Answer 1

The first law of thermodynamics states the equivalence of heat and work. This law is based on the principle of conservation of energy.

The internal energy U of a system can change through two modes of energy transfer: heat and work.

Let ∆Q = Heat supplied to the system by the surroundings,

∆W = Work done by the system on the surroundings.

∆U = Change in internal energy of the system.

From the general principle of conservation of energy,

i.e.,

∆Q = ∆U + ∆W ....(1)

The energy ∆Q, supplied to the system goes in partly to increase the internal energy of the system (∆U) and work (∆W). Equation (1) is called the first law of Thermodynamics. This is the general law of conservation of energy applied to any system in which the energy transfer from or to the surroudnings. We can write equation (1) as

∆Q - ∆W = ∆U ......(2)

Now, the system go from an initial state to final state in a number of ways. To change the state of a gas from (P₁, V₁) to (P₂, V₂), we first change the volume from V₁ to V₂, keeping the pressure constant. This means that we first go to state (P₁, V₂). Changing the pressure from P₁ and P₂, keeping volume constant to the state (P₂, V₂). We can also first keep the volume constant and then keep the pressure constant. U is a state variable. ∆U depends only on the initial and final states and not on the path taken by the gas to move from one to the other.

However, ∆Q and ∆W depends on the path in moving from initial to final states.

From equation (2), (∆Q - ∆W) is path independent for a system with ∆U = 0,

∆Q = ∆W

This implies that heat supplied to the system is completely used up by the system in doing work on the environment. Work done by the system against a constant pressure P is

∆W = P ∆V

Here, ∆V is the small change in volume of gas.

So equation (2) gives

∆Q = ∆U + P∆V .......(3)