First Law of thermodynamics

The first law of thermodynamics states that whenever heat is added to a system, the heat will transform to some other form of energy in the same amount. 

In this lesson, you will learn to understand the equation Q = ∆E - W or Q = ∆E + W

First law of thermodynamics

A system could be anything where heat is being added to include the following:

  • A steam engine that will power a train or a vehicle
  • A steam turbine that will generate electricity
  • Your body
  • A pressure cooker

What happens then when you add heat to a system?

This heat can either increase the internal energy of the system if it does not leave the system, do external work if it leaves the system or do a combination of both.

We can then restate the first law of thermodynamics as shown below.

Heat added to a system = increase in internal energy of the system + external work done by the system.

An important thing to keep in mind about the first law of thermodynamics!

Keep in mind that if the system does no work, the internal energy will keep on increasing. By the same token, the pressure inside the system will increase as well. This may become very dangerous since if the system cannot tolerate the constant increase of pressure, it may explode.

Imagine a pressure cooker built in a way so that no steam will be allowed to escape! The internal energy will get higher and higher and this may eventually create an explosion.

That is why a pressure cooker is built with a safety feature. This safety feature is usually a spring-loaded valve that will allow some of the steam to escape.

As the steam is coming out, it does some work on the valve by raising the weight of the valve. Thus, heat has been converted to mechanical energy.

Mathematical formulation of the first law of thermodynamics

Let Q = the net quantity of heat the system received

Let ΔE = increase in internal energy or generally speaking change in internal energy.

Let W = work done by the system. We can then rewrite the 1st law of thermodynamics as shown below.

Q = ΔE + w

Subtract w from both sides

Q - w = ΔE + w - w

ΔE = Q - w

The formula above represents work done by the system.

The work done on the system is the negative of the work done by the system.

The figure below mentioned earlier shows the first law of thermodynamics when a pressure cooker is heated.

First law of thermodynamics
When the work is done on the system, the formula to use is

ΔE = Q + w

Why the work done on the system is always the negative of the work done by the system

Why ΔE = Q + w when work is done on the system?

When work is done on the system, the internal energy of the system tends to increase.

However, if we don't turn Q - w into Q + w, we will end up with a contradiction as shown below

Suppose ΔE = Q - w

If Q = 0, ΔE = -w

The negative number next to w shows decrease not increase of internal energy.

It is like going from 8 joules to 6. Change in energy is 6 - 8 = -2

Since -2 is a negative number, it shows that the energy has been decreased.

By the same token, -w shows that the energy has been decreased.

Heat is not the only way to create change in internal energy

Adding heat is not the only to increase or decrease the internal energy of a system. Let Q  = 0

Work can be done on a system by compressing it. 

ΔE = 0 + w

ΔE = w

In this case, the work will cause an increase in energy and thus an increase in temperature without using any heat input.

An example of this is when you are using a bicycle pump. When pumping the handle, you are doing work on the system. If you touch the pump, you will see that it is a little hot although no heat was added to the pump. This is because you increase the internal energy of the pump while you were doing work on the system.

However, if work is done by the system, we get ΔE = 0 - w

ΔE = -w

The internal energy in this case will decrease.

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