1. First law of thermodynamics:

• The first law of thermodynamics, known as the law of energy conservation, states that energy cannot be created or destroyed, only converted from one form to another.
• [math]Q = ∆U + W[/math]

  
  Figure 1 First law of thermodynamics

• Where:
• – Q (heat) is the energy added to or removed from a system
• – ∆U (change in internal energy) is the change in the system’s internal energy
• – W (work) is the energy transferred to or from a system through work
• This equation indicates that the heat added to or removed from a system is equal to the change in internal energy plus the work done on or by the system.
• – Q (energy transferred to the system by heating) is the energy added to the system through heat transfer.
• – ∆U (increase in internal energy) is the change in the system’s internal energy, which includes changes in kinetic energy, potential energy, and potential energy associated with molecular interactions.
• – W (work done by the system) is the energy transferred from the system to its surroundings through work, such as expanding against a pressure or moving an object.
• – In essence, the equation states that the energy transferred to a system through heating (Q) is equal to the increase in internal energy (∆U) plus the work done by the system (W).
• This equation is a fundamental principle in thermodynamics and is widely applied in various fields, such as engineering, chemistry, and physics.
• Example
• – Suppose we have a gas in a cylinder with a movable piston. We heat the gas by adding 100 J of heat (Q = 100 J). The gas expands, doing 50 J of work (W = -50 J) on the surroundings. What is the change in internal energy (∆U)?
• Given data:
• Heat = Q = 100 J
• Work done by the system = -50 J
• Find data:
• Internal energy of the system = ∆U =?
• Formula:
• [math]Q = ∆U + W[/math]
• Solution:
• [math]\begin{gather}
  Q = \Delta U + W \\
  \Delta U = Q – W \\
  \Delta U = 100 – (-50) \\
  \Delta U = 150 \, \text{J}
  \end{gather} [/math]
• So, the internal energy of the gas has increased by 150 J.
• ⇒ Positive Work Done (Work done BY the system):
• Expansion of a gas:
• – When a gas expands against a pressure, it does work on its surroundings. For example, in a cylinder, if the gas expands from V1 to V2, the work done is:
• [math]W = P (V2 – V1)[/math]
• Where P is the pressure and V1 and V2 are the initial and final volumes.
• Lifting an object:
• When an object is lifted, the system (the person or machine) does work on the object. The work done is:
• [math]W = mgh [/math]
• Where m is the mass of the object, g is the acceleration due to gravity, and h is the height lifted.
• ⇒Negative Work Done (Work done ON the system):
• Compression of a gas:
• When a gas is compressed, work is done on the system. For example, in a cylinder, if the gas is compressed from V1 to V2, the work done is:
• [math]W = -P (V2 – V1)[/math]
• Note the negative sign, indicating work done on the system.
• Pushing an object:
• When an object is pushed, work is done on the system (the object).
• Note the negative sign, indicating work done on the system.
• Pushing an object:
• When an object is pushed, work is done on the system (the object). The work done is:
• [math]W = -Fd [/math]
• Where F is the force applied and d is the distance pushed.
• Remember, the sign convention is:
• – Positive work: Work done BY the system (expansion, lifting)
• – Negative work: Work done ON the system (compression, pushing)
• 

• Figure 2 Positive and negative working of gas molecules

2. Applications of first law of thermodynamics:

• The First Law of Thermodynamics has numerous applications in various fields, including:
• Thermal Engineering:
• Design and optimization of heat engines, refrigeration systems, and heat pumps.
• Power Generation:
• Efficiency analysis of power plants, such as fossil fuel-based and nuclear power plants.
• Refrigeration and Air Conditioning:
• Design and optimization of refrigeration systems, air conditioners, and heat exchangers.
• Aerospace Engineering:
• Analysis of aircraft and rocket propulsion systems, including fuel efficiency and energy conversion.
• Chemical Engineering:
• Energy balance and efficiency analysis in chemical reactions and processes.
• Materials Science:
• Study of phase transitions, such as melting and boiling, and the associated energy changes.
• Biology:
• Understanding the energy conversion and utilization in living organisms, such as metabolism and respiration.
• Food Processing:
• Energy efficiency analysis in food processing, packaging, and storage.
• Building Design:
• Energy-efficient building design, insulation, and heating/cooling systems.
• Transportation:
• Fuel efficiency analysis and optimization in vehicles, including electric and hybrid vehicles.
• Energy Storage:
• Analysis and optimization of energy storage systems, such as batteries and supercapacitors.
• Cryogenics:
• Energy efficiency analysis in cryogenic systems, such as liquefaction and storage of gases.
• Fuel Cells:
• Efficiency analysis and optimization of fuel cell systems.
• Solar Energy:
• Energy conversion and efficiency analysis in solar panels and solar thermal systems.
• Geothermal Energy:
• Energy conversion and efficiency analysis in geothermal power plants.
• These applications involve the analysis and optimization of energy conversion, storage, and utilization, all of which are governed by the First Law of Thermodynamics.

Non-flow processes

• Non-flow processes, also known as closed-system processes, are thermodynamic processes where the system is bounded and does not exchange matter with its surroundings.
• Non-flow processes are important in thermodynamics because they help us understand the energy interactions between a system and its surroundings, without the complication of matter transfer.

3. Isothermal, adiabatic, constant pressure and constant volume changes.

• Isothermal Process:
• “A process that occurs at a constant temperature (T). During an isothermal expansion or compression, the system’s temperature remains constant, and the heat transfer (Q) is equal to the work done (W)”.
• [math] ∆U = 0 (\text{since T is constant}) \\ Q = W [/math]
• 
• Figure 3 Isothermal process
• Adiabatic Process:
• “A process that occurs without heat transfer (Q = 0). In an adiabatic expansion or compression, the system’s temperature changes, and the work done (W) is equal to the change in internal energy (∆U)”.
• [math] Q = 0 \\ W = ∆U[/math]
• Figure 4 Adiabatic process
• Constant Pressure Process:
• “A process that occurs at a constant pressure (P). During a constant pressure expansion or compression, the system’s pressure remains constant, and the work done (W) is equal to the product of the pressure and the change in volume (ΔV)”.
• [math]W = PΔV [/math]
• 
• Figure 5 Constant pressure process in thermodynamic process
• Constant Volume Process:
• “A process that occurs at a constant volume (V). During a constant volume expansion or compression, the system’s volume remains constant, and the work done (W) is zero, since there is no change in volume”.
• [math] W = 0 \text{(since ΔV = 0)} [/math]
• 
• Figure 6 Constant volume process in thermodynamic process
• These processes are important concepts in thermodynamics, and understanding them helps us analyze and predict the behavior of systems in various situations.

4. Ideal gas Law:

• The ideal gas law is a fundamental principle in physics that describes the behavior of ideal gases. It’s a mathematical relationship that connects the pressure, volume, temperature, and number of moles of an ideal gas.
• [math]pV = nRT [/math]
• Where:
• – p is the pressure of the gas (measured in pascals, Pa)
• – V is the volume of the gas (measured in cubic meters, m³)
• – n is the number of moles of gas present (measured in moles, mol)
• – R is the gas constant (approximately 8.3145 joules per mole-kelvin, )
• – T is the temperature of the gas in kelvin (K)
• This equation states that the product of the pressure and volume of an ideal gas is equal to the product of the number of moles of gas, the gas constant, and the temperature.
• – Pressure (p): The force exerted per unit area on the gas. Increasing pressure compresses the gas.
• – Volume (V): The space occupied by the gas. Increasing volume expands the gas.
• – Moles (n): The amount of gas present. Increasing moles adds more gas molecules.
• – Gas constant (R): A constant value relating energy to temperature.
• – Temperature (T): A measure of the average kinetic energy of the gas molecules. Increasing temperature increases the energy.
• 
• Figure 7 Ideal gas Law
• [math] \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} [/math]
• The ideal gas law has several important implications:
• – If pressure and temperature remain constant, increasing the volume will proportionally increase the number of moles.
• – If volume and temperature remain constant, increasing the pressure will proportionally decrease the number of moles.
• – If pressure and volume remain constant, increasing the temperature will proportionally increase the number of moles.
• This equation is a powerful tool for understanding and predicting the behavior of ideal gases in various situations, such as:
• – Gases in containers
• – Gases in the atmosphere
• – Gases in industrial processes
• – Gases in biological systems
• Keep in mind that the ideal gas law assumes ideal behavior, which isn’t always the case in real-world scenarios. However, it provides a useful approximation for many applications.

5. Adiabatic process:

• In adiabatic equation
• [math]pV^γ=constant [/math]
• Where:
• – p is the pressure of the gas
• – V is the volume of the gas
• – γ (gamma) is the adiabatic index, which is the ratio of specific heats (cp/cv) and is approximately 1.4 for air
• Figure 8 Adiabatic process curve
• This equation describes the relationship between pressure and volume for an adiabatic process, which is a process that occurs without heat transfer. In other words, the system is thermally insulated.
• – No heat transfer (Q = 0)
• – Work is done on or by the system
• – The process is reversible
• The adiabatic equation shows that:
• – If the pressure increases, the volume decreases, and vice versa
• – The constant value is a function of the initial conditions of the system
• This equation is important in understanding various phenomena, such as:
• – Adiabatic expansion and compression of gases
• – Sound waves and acoustic phenomena
• – Atmospheric science and weather patterns
• – Engine performance and efficiency

6. Isothermal process:

• An isothermal change is a process that occurs at a constant temperature (T). During an isothermal change, the system’s temperature remains constant, and the heat transfer (Q) is equal to the work done (W).
• The equation for an isothermal change is:
• [math]pV = constant[/math]
• Where:
• – p is the pressure of the gas
• – V is the volume of the gas
• This equation states that the product of the pressure and volume of an ideal gas remains constant during an isothermal change.
• 
• Figure 9 Isothermal process (in volume change due to pressure of gas molecules at constant temperature)
• Observation of an isothermal change:
• Initial State:
• – First container pressure of the gas molecules ([math]p_1[/math])
• – Volume of the molecules in 1^st container ([math]V_1[/math])
• – Constant Temperature (T)
• Final State:
• – Second container pressure ([math]p_2[/math])
• – Volume of second con ([math]V_2[/math])
• – Temperature (T) (remains constant)
• Since it’s an isothermal change, (temperature of both container remains constant) [math]T_1 = T_1 = T[/math]
• Using the ideal gas law:
• [math] \\ p_1 V_1 = nRT  \\ p_2 V_2 = nRT[/math]
• Since T is constant, we can set up the equation
• [math]p_1 V_1 = p_2 V_2[/math]
• This simplifies to:
• [math]pV = constant[/math]
• This equation shows that during an isothermal change, the product of pressure and volume remains constant.
• Note that this equation only applies to ideal gases and may not accurately model real-world scenarios. However, it provides a useful approximation and insight into isothermal changes.

7. Work done at constant pressure:

• At constant pressure, the work done (W) is equal to the pressure (p) times the change in volume (ΔV):
• [math]W = pΔV[/math]
• Substituting this into the first law equation, we get:
• [math]ΔU = Q – pΔV[/math]
• This equation shows that the change in internal energy (ΔU) is equal to the heat added (Q) minus the work done () at constant pressure.
• Applications of this equation include:
• – Isothermal expansion:
• When a gas expands at constant temperature, the heat added (Q) is used to do work (), and the internal energy (U) remains constant.
• – Adiabatic expansion:
• When a gas expands without heat transfer (Q=0), the work done (pΔV) is done at the expense of internal energy (U), which decreases.
• – Constant pressure processes:
• Many chemical reactions and biological processes occur at constant pressure. This equation helps us understand the energy changes during these processes.
• – Engine cycles:
• The equation is used to analyze the efficiency of engine cycles, such as the Carnot cycle and Otto cycle.
• – Thermodynamic systems:
• This equation is used to study the energy behavior of thermodynamic systems, such as refrigeration systems and heat pumps.
• This equation is a fundamental tool for understanding and analyzing various thermodynamic processes that occur at constant pressure.