Thermodynamics Unit-II: First Law

First Law of Thermodynamics

• The first law of thermodynamics states that energy cannot be created or destroyed, only converted from one form to another.
• The law can be mathematically expressed as: Q - W = ΔE (energy transferred as heat minus energy transferred as work equals the change in internal energy)
• The law is based on experimental observations and cannot be proved mathematically.

Energy Transfer Mechanisms

• Heat (Q): energy transferred due to a temperature difference between the system and its surroundings.
• Work (W): energy transferred when a force is applied over a distance or when a system changes its volume under pressure.

Energy Conservation in a Closed System

• For a closed system, the total energy (kinetic, potential, and internal energies) remains constant, although it can change forms.
• The energy balance needs to account for the energy carried by the mass entering and leaving the system.

Law of Conservation of Energy

• The law of conservation of energy states that the total energy in an isolated system remains constant over time, although energy can transform from one form to another.
• This fundamental principle of physics implies that energy cannot be created or destroyed, only converted or transferred.

Joule's Experiment

• James Prescott Joule's experiment demonstrated the mechanical equivalent of heat.
• The experiment showed that mechanical work could be converted into heat, providing strong evidence for the conservation of energy.

Energy as a Property of a System

• Energy is a property of a thermodynamic system, meaning it is a state function that describes the energy content of the system.
• Energy is a scalar quantity that encompasses various forms, including kinetic, potential, internal, thermal, chemical, electrical, nuclear, and radiant energy.

Internal Energy

• Internal energy (U) is a fundamental concept in thermodynamics that represents the total energy contained within a system.
• Internal energy is a state function that depends on the temperature of the system.
• For an ideal gas, internal energy (U) is a function of temperature (T) only.

Enthalpy

• Enthalpy (H) is a thermodynamic property that represents the total energy of a system.
• Enthalpy is defined as: H = U + PV, where U is the internal energy, P is the pressure, and V is the volume.
• Enthalpy is a useful concept for analyzing thermodynamic systems, especially in chemical engineering and chemistry.

Specific Heats

• The specific heat is defined as the energy required to raise the temperature of a unit mass of a substance by one degree.
• There are two kinds of specific heats: specific heat at constant volume (Cv) and specific heat at constant pressure (Cp).
• Cp is always higher than Cv because at constant pressure the system is allowed to expand and energy for this expansion must also be supplied to the system.

First Law of Thermodynamics for Non-Flow Processes

• The First Law of Thermodynamics can be applied to non-flow processes, also known as closed systems or batch processes.
• The First Law for a closed system is: ΔE = Q - W, where ΔE is the change in internal energy, Q is the heat added to the system, and W is the work done on the system.

Examples of Non-Flow Processes

• Heating a solid: heat is added, and the internal energy increases.
• Compression of a gas: work is done on the system, and the internal energy increases.
• Phase change: heat is added, and the internal energy increases.
• Expansion of a gas: work is done by the system, and the internal energy decreases.
• Cooling a solid: heat is removed, and the internal energy decreases.

Isothermal and Adiabatic Processes

• Isothermal process: a process in which the temperature remains constant, and no heat is added or removed.
• Adiabatic process: a process in which there is no heat transfer between the system and the surroundings, and the internal energy changes due to work done on or by the system.### Work Done in Different Scenarios

Work Done in Compressing a Gas

• Work done on the system: W = -PdV (negative sign indicates work done on the system)
• Force applied by piston: F = PA (where P is pressure and A is area)
• Displacement of piston: dx = dV/A (where dV is change in volume)
• Work done: W = Fdx = PAdx = PdV

Work Done in Expanding a Gas

• Work done by the system: W = PdV (positive sign indicates work done by the system)
• Force applied by gas: F = PA
• Displacement of piston: dx = dV/A
• Work done: W = Fdx = PAdx = PdV

Work Done in Lifting a Weight

• Work done by force applied to lift weight against gravity: W = mgh (where m is mass, g is acceleration due to gravity, and h is height lifted)
• Force lifting weight: F = mg
• Displacement of weight: h (height lifted)
• Work done: W = Fdh = mgh

Work Done in Stirring or Agitation

• Work done by stirrer or agitator: W = τθ (where τ is torque and θ is angular displacement)
• Torque applied: τ
• Angular displacement: θ
• Work done: W = τdθ = τθ

Work Done in Isothermal and Adiabatic Processes

• Isothermal compression or expansion: W = 0 (no work is done since process occurs at constant temperature and pressure)
• Adiabatic compression: W = -PdV (compression)
• Adiabatic expansion: W = PdV (expansion)
• Sign convention for work done:
  • Negative sign (-) indicates work done on the system
  • Positive sign (+) indicates work done by the system

Understand the First Law of Thermodynamics, which states that energy gained by a system is equal to energy lost by its surroundings. Learn about energy transfer through heat and work in closed systems.