First Law of Thermodynamics

Thermodynamics encompasses the processes in which energy is transferred as heat and work. As explored in earlier chapters, work occurs when energy is transferred between objects through mechanical means. Similarly, heat is energy transferred due to a difference in temperature. This section focuses on the distinction between these two forms of energy transfer: while heat is the transfer of energy caused by temperature differences, work is energy transferred in a manner not influenced by temperature disparities.

In the study of thermodynamics, we commonly refer to systems, which are defined as any object or group of objects under consideration. The external environment or surroundings refers to everything else that is not part of the system.

The first law of thermodynamics governs energy interactions within systems, stating:

Energy can be converted from one form to another through the interactions of heat, work, and internal energy. However, energy cannot be created or destroyed under any circumstances.

Mathematically, this principle is expressed as:

$dQ = dU + dW$

where:

• $dQ$ represents the heat exchanged between a system and its surroundings,
• $dU$ is the change in internal energy of the system,
• $dW$ is the work done by or on the system.

Thermodynamic Processes

Before delving into thermodynamic processes, it is crucial to define the thermodynamic state of a system. A system's state is characterized by properties such as temperature, pressure, and volume. The instantaneous values of these properties define the system's state. For instance, a thermos flask containing water at a specific temperature and pressure represents a particular state. If these properties change—such as by adding 50 mL of water at 25°C—the state of the system also changes.

A thermodynamic process refers to any change in the state of a thermodynamic system. For example, in a car engine, heat is generated by the chemical reaction between oxygen and vaporized gasoline within the engine cylinder. The heated gases then push the pistons inside the cylinder, performing mechanical work that powers the car.

Specific Heat Capacity

In thermodynamic processes, we are concerned with how much heat transfer can alter the temperature of a system. The extent of this change depends on the nature of the system. A physical quantity that describes a system's ability to absorb heat and consequently increase in temperature is termed specific heat capacity.

Let a body of mass $m$ be initially at temperature $T$. If its temperature increases from $T$ to a higher value, the heat required to induce this temperature change is related to its specific heat capacity.

1. Molar Specific Heat Capacity The molar specific heat capacity refers to the amount of heat required to raise the temperature of one mole of a material by 1°C at constant pressure or constant volume. If $n$ represents the number of moles of a substance, and the heat required to raise its temperature by $\Delta T$ is $Q$, the molar specific heat capacity, $C$, is given by: $C = \frac{Q}{n \cdot \Delta T}$

2. Specific Heat Capacity of Gases The specific heat capacity of an ideal gas does not depend on the nature of the gas but is influenced by the conditions under which heat is supplied. These conditions could be constant volume or constant pressure. In practical terms, this means that the specific heat capacity of a gas will vary depending on whether the process occurs at constant volume or constant pressure.

   Consider an ideal gas in a cylinder with a frictionless piston, where the internal temperature, volume, and pressure are $T$, $V$, and $P$, respectively. Under these conditions, the specific heat capacity is determined by the type of thermodynamic process the gas undergoes, either at constant pressure or constant volume.

Work done during thermodynamic processes

The process occurring in closed systems which do not permit the transfer of mass across their boundaries is known as non-flow process. In non-flow process, there is only work and heat transfer but there is no mass transfer into or out of the system. During the energy flow, some of the changes take place in pressure, volume, temperature, internal energy, heat, work etc.

Thermodynamic Processes

a. Isochoric Process (Constant Volume)

An isochoric process is a thermodynamic process in which the volume remains constant. When a gas is heated in a closed, rigid container, the pressure and temperature increase, but no work is done since the volume does not change:

$$dW = 0$$

Hence, by the first law of thermodynamics, all the heat energy supplied contributes to an increase in the system's internal energy:

$$dQ = dU = C_V (T_2 - T_1)$$

• $dQ$ = heat supplied
• $dU$ = change in internal energy
• $C_V$ = molar specific heat capacity at constant volume
• $T_1, T_2$ = initial and final temperatures respectively

b. Isobaric Process (Constant Pressure)

An isobaric process occurs when a gas is heated or cooled at constant pressure. During this process, both the temperature and volume of the gas change. The gas performs or absorbs work:

$$dQ = dU + dW = C_P (T_2 - T_1)$$

• $C_P$ = molar specific heat capacity at constant pressure

This process is common in atmospheric and engineering systems, such as internal combustion engines.

c. Isothermal Process (Constant Temperature)

In an isothermal process, the temperature of the system remains constant. Therefore, the internal energy of an ideal gas (which depends only on temperature) does not change:

$$dU = 0 \Rightarrow dQ = dW$$

All the heat supplied to the system is converted into work done by the gas, or vice versa.

Conditions for an Isothermal Process:

1. The gas must be in a thin-walled, thermally conductive vessel.
2. The gas must be in thermal contact with a constant-temperature bath.
3. The process must occur very slowly to maintain constant temperature.

d. Adiabatic Process (No Heat Exchange)

An adiabatic process is characterized by no heat exchange between the system and its surroundings:

$$dQ = 0$$

Applying the first law of thermodynamics:

$$0 = dU + dW \Rightarrow dW = -dU$$

In adiabatic expansion, the system does work at the expense of its internal energy, causing a drop in temperature. Conversely, in adiabatic compression, work done on the system increases internal energy and raises the temperature.

e. Applications of the First Law of Thermodynamics

The first law of thermodynamics is a fundamental statement of energy conservation. Some practical applications include:

i. Internal Combustion Engines

In automobile engines, chemical energy stored in fuel is converted into mechanical work and heat through combustion. According to the first law:

$$\text{Energy input (chemical)} = \text{Mechanical work output} + \text{Thermal energy output}$$

The heat not converted into work is dissipated via exhaust gases, coolant fluids, and radiation.

ii. Electric Power Generation

Hydroelectric plants convert the gravitational potential energy of water into mechanical energy via turbines, then into electrical energy through generators. The energy output is balanced by mechanical energy input minus losses:

$$\text{Electrical energy output} \leq \text{Mechanical energy input}$$