Zeroth Law of Thermodynamics & First Law of thermodynamics

What is the Zeroth Law of thermodynamics?

Zeroth law of thermodynamics states that “if two systems are equal in temperature to a third system, they are all equal in temperature to each other”.

According to Wikipedia: “The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third one, then they are in thermal equilibrium with each other. Accordingly, the thermal equilibrium between systems is a transitive relation”.

For better understanding let’s assume there are three bodies A, B & C. The temperature of the body “A” equal to body “B”. And the temperature of body “B” is also equal to body “C”. Then ultimately the temperature of the body “A” equals to body “C”.

Zeroth law of thermodynamics was expressed by R.H. Fowler in the year 1931. However, since the first law of thermodynamics and the second law of thermodynamics already existed at that time, It was known as the Zeroth law of thermodynamics.

The zeroth law of thermodynamics provides the basis for temperature measurement by comparing the temperature of two bodies A and B with the help of the third body C without actually bringing body A and B in thermal contact. In practice, Body C in the zeroth law is called the Thermometer.

First Law of thermodynamics

First Law of thermodynamics states “Heat and work are mutually convertible but since energy can neither be created nor destroyed, the total energy associated with an energy conversion remains constant.” Or “When a system undergoes a thermodynamic cycle then the net heat supplied to the system from the surroundings is equal to the net-work done by the system to the surroundings”

Experiment for checking the first law of thermodynamics:

The change of temperature of the fluids in an insulated container is measured by a thermometer while the work input to the paddle wheel is measured by the fall of the weight as shown in the figure.

We already know that temperature rise can also be obtained by heat transfer.

And the experiment shows:

(1). A definite quantity of work is always required to accomplish the same temperature rise obtained with a unit of amount of heat.

(2). The temperature of the liquid is raised by the by work-done or heat transfer, the liquid can be returned by the heat transfer in the opposite direction to be the initial state.

The above result leads to the conclusion that work and heat are different forms of something known as Energy.

It can be stated that whenever a physical system passes through a complete cycle the algebraic sum of the work transfers during the cycle $\oint dW$ bears a definite ratio to the algebraic sum of the heat transfers during the cycle $\oint dQ$ .

This may be expressed as $\oint dW = J \oint dQ$

where J is the proportional constant and known as Mechanical equivalent of Heat. The unit of this constant is Nm/J in Si units.

First Law of thermodynamics to a process

The change in stored energy of the system is numerically equal to the net heat minus net work-done interactions during a process. ( Heat added to the system will be considered as positive and heat removed from the system, as negative.)

$\therefore Q - W = E_2 - E_1$

$Q - W = \Delta E$

or $\int_1^2 d \left( Q-W \right) = \Delta E = E_2 - E_1$

Let’s assume, changes in potential and kinetic energies for a closed system are neglected and the magnetic, chemical and electric energies are absent, the above equation may be written as:

$\int_1^2 d\left(Q - W \right) = \Delta U = U_2 - U1$

$Q - W = \Delta U = U_2 - U_1$

where U represents the internal energy.

When heat is added to a system its temperature and internal energy rises and external work performed due to increasing the volume of the system.

Energy as a property of a system

Consider a system undergoes to a cycle process in which it changes its state from 1 to state 2 by following path A, and returns from state 2 to 1 by path B.

Equation the first law for path A as

$Q_A = \Delta E_A + W_A$ ……(1)

and for path B as

$Q_A = \Delta E_A + W_A$ …….(2)

The processes A and B together complete the cycle, for which

$\oint dW = \oint Q$

⇒ $W_A + W_B = Q_A + Q_B$

or $Q_A - W_B = W_B - Q_B$ …….(3)

Putting the value of $Q_A$ and $Q_B$ from equation (1) & (2) in the equation (3)

We get :
$\Delta E_A + W_A -W_A = W_B - \left( \Delta E_B + W_B \right)$

$\Rightarrow \Bold{\Delta E_A = - \Delta E_B}$ …..(4)

Similarly, if the system returned from state 2 to state 1 by following path C instead path B, We had

$\Bold{ \Delta E_A = - \Delta E_C}$ …….(5)

Thus, it is seen that the change in energy between two states of a system is always same whatever the path is taken to change the state. Therefore, the energy has a definite value for every state of the system. Hence, it is a point function and a property of a system.