6.4 First Law of Thermodynamics

6.4 First Law of Thermodynamics

When heat is added to a system there is an increase in the internal energy due to the rise in temperature, an increase in pressure or change in the state. If at the same time, a substance is allowed to do work on its environment by expansion, the heat $Q$ required will be the heat necessary to change the internal energy of the substance from $U_{1}$ in the first state to $U_{2}$ in the second state plus the work $W$ done on the environment.

Thus $Q = (U_{2} - U_{1}) + W$

or

Thus the change in internal energy $\Delta U = U_{2} - U_{1}$ is defined as $Q - W$. Since it is the same for all processes concerning the state, the first law of thermodynamics, thus can be stated as:

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In any thermodynamic process, when heat $Q$ is added to a system, this energy appears as an increase in the internal energy $\Delta U$ stored in the system plus the work $W$ done by the system on its surroundings.

1. Conservation Principle: The underlying principle of the first law of thermodynamics is the conservation of energy. It asserts that while energy can change from one form to another (such as from chemical potential energy to thermal energy), the total energy in an isolated system remains constant over time.

2. Wider Applicability: Beyond mechanical systems, the first law of thermodynamics applies universally to all forms of energy and all types of processes, including chemical reactions, electrical systems, and nuclear reactions. It provides a foundational understanding that allows scientists and engineers to predict and understand energy transformations in various contexts.

The first law of thermodynamics expresses the law of conservation of energy by affirming that energy is a conserved quantity. In isolated systems, it provides a framework to understand how energy is transferred and transformed within systems without violating the fundamental principle that energy neither be created nor be destroyed.

A bicycle pump is a good example of first law of thermodynamics. When we pump on the handle rapidly, it becomes hot due to mechanical work done on the gas, raising thereby its internal energy. One such simple arrangement is shown in Fig. 6.6. It consists of a bicycle pump with a blocked outlet.

A thermocouple connected through the blocked outlet allows the air temperature to be monitored. Thermocouple thermometer can detect a minute variation of the temperature. When the piston is rapidly pushed, thermometer shows a temperature rise due to increase of internal energy of the air. The push force does work on the air, thereby, increasing its internal energy, which is shown by the increase in temperature of the air.

Human metabolism also provides an example of energy conservation. Human beings and other animals do work when they walk, run, or move. Work requires energy. Energy is also needed for growth to make new cells and to replace old cells that have died. Energy transforming processes that occur within an organism are named as metabolism. We can apply the first law of thermodynamics ($\Delta U = Q - W$), to an organism of the human body. Work done will result in the decrease in internal energy of the body. Consequently, the body temperature or in other words internal energy is maintained by the food we eat.

Example 6.2

A gas is enclosed in a container fitted with a piston of cross-sectional area $0.10\,\mathrm{m^{2}}$. The pressure of the gas is maintained at $8000\,\mathrm{N\,m^{-2}}$. When heat is slowly transferred, the piston is pushed up through a distance of $4.0\,\mathrm{cm}$. If $42\,\mathrm{J}$ heat is transferred to the system during the expansion, what is the change in internal energy of the system?

Solution

The work done by the gas is:

The change in internal energy is found from first law of thermodynamics: