Laws of Thermodynamics

The Zeroth Law of Thermodynamics establishes a fundamental principle of thermal equilibrium. It states that if two objects are each in thermal equilibrium with a third object, they must also be in thermal equilibrium with each other. This principle allows for the definition of temperature and enables the comparison of thermal states between different systems. Essentially, it forms the basis for the concept of temperature as a measurable property, ensuring that if two systems are equal in temperature with a third, they are equal in temperature with each other.

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed. In a closed system, the change in internal energy (ΔU) is determined by the heat added to the system (Q) and the work done by the system (W). Specifically, it can be expressed as ΔU = Q - W. Here, if heat is added to the system, it increases the internal energy, while work done by the system (e.g., expanding against an external pressure) reduces it. This relationship emphasizes the conservation of energy principle in thermodynamic processes.

In thermodynamics, the change in internal energy of a system can be calculated using the first law of thermodynamics, which states: ΔU = Q + W. Here, Q is the heat added to the system (2500 J) and W is the work done on the system (1800 J). By substituting the values, we get ΔU = 2500 J + 1800 J = 4300 J. This indicates that the internal energy of the system increases by 4300 J due to the combined effects of added heat and work.

In thermodynamics, when work is done on a gas during expansion or compression at constant pressure, it is defined as negative because the system is losing energy to the surroundings. The equation W = -PΔV indicates that when the volume of the gas decreases (ΔV is negative), work is done on the gas, and when the volume increases (ΔV is positive), work is done by the gas. The negative sign reflects the convention that work done on the system is considered positive, while work done by the system is negative.

For a monatomic ideal gas, the molar specific heat at constant volume (Cv) is derived from the degrees of freedom of the gas particles. A monatomic gas has three translational degrees of freedom, contributing to its internal energy. According to the equipartition theorem, each degree of freedom contributes (1/2)R per mole to the heat capacity. Therefore, with three degrees of freedom, the total contribution is (3/2)R, which represents the molar specific heat at constant volume for a monatomic ideal gas.

An adiabatic process is characterized by the absence of heat transfer between a system and its surroundings. This means that any change in the internal energy of the system is due solely to work done on or by the system, rather than heat exchange. In such processes, temperature and pressure can change, but the defining feature is that there is no heat flow, making it distinct from isothermal (constant temperature) or isobaric (constant pressure) processes.

In an isovolumetric process, the volume of the system remains constant, which means no work is done on or by the system (W = 0). According to the first law of thermodynamics, the change in internal energy (ΔU) is equal to the heat added to the system (Q) since the work done is zero. Therefore, during this process, all the heat transfer results in a change in internal energy, leading to the relationship ΔU = Q.

For a monatomic ideal gas, the specific heat at constant pressure (Cp) and the specific heat at constant volume (Cv) are related through the equation Cp - Cv = R, where R is the ideal gas constant. This relationship arises from the first law of thermodynamics and the definitions of Cp and Cv. For monatomic gases, the degrees of freedom are limited, leading to this specific difference in heat capacities, which reflects how energy is stored and transferred in the gas under different conditions.

In an adiabatic process, there is no heat exchange with the surroundings (Q = 0). According to the First Law of Thermodynamics, which states that the change in internal energy (ΔU) is equal to the heat added to the system (Q) minus the work done by the system (W), this simplifies to ΔU = 0 - W. Thus, the change in internal energy is equal to the negative of the work done by the system, leading to the expression ΔU = -W.

In an isobaric process, the pressure remains constant while the volume changes. On a PV diagram, where the x-axis represents volume and the y-axis represents pressure, a constant pressure results in a horizontal line. This indicates that as the volume increases or decreases, the pressure does not change, visually demonstrating the relationship between volume and pressure during the process.

To determine the change in volume of the gas, we can use the first law of thermodynamics, which states that the change in internal energy (ΔU) equals the heat added to the system (Q) minus the work done by the system (W). Here, ΔU is 3.0 × 10³ J and Q is 4.2 × 10³ J. The work done at constant pressure can be calculated using W = PΔV. Rearranging the equation gives ΔV = (Q - ΔU) / P. Substituting the values leads to a change in volume of 1.2 × 10⁻² m³.

In a reversible isothermal process, the temperature of the gas remains constant while it is compressed. According to the first law of thermodynamics, any work done on the gas during compression must be balanced by a corresponding heat transfer. Since work is done on the gas, its internal energy would increase, leading to an increase in temperature. To maintain constant temperature, heat must flow out of the gas, thus it "leaves" the gas. This heat loss compensates for the work done on the gas, ensuring thermal equilibrium.

In an adiabatic process, no heat is exchanged with the surroundings, and the relationship between pressure (P) and volume (V) of an ideal gas is governed by the specific heat capacities. The ratio γ (gamma) is defined as the ratio of the specific heat at constant pressure (Cp) to the specific heat at constant volume (Cv). This ratio is crucial in determining how the gas will behave under adiabatic conditions, influencing the temperature and pressure changes during the process. Thus, γ = Cp / Cv is the appropriate definition.

The First Law of Thermodynamics asserts that energy cannot be created or destroyed, only transformed from one form to another. This principle emphasizes the conservation of energy within a closed system, meaning that the total energy remains constant over time. Any energy input into the system must equal the sum of the energy output and the change in internal energy. This foundational concept underlies various physical processes, reinforcing the idea that energy is conserved in all interactions.