3.1 Energy, heat, and work

Energy, heat, and work are fundamental concepts in thermodynamics. They're the building blocks for understanding how energy flows and changes in systems. This topic lays the groundwork for grasping the First Law of Thermodynamics, which is all about energy conservation.

The First Law states that energy can't be created or destroyed, only transformed. By exploring energy, heat, and work, we'll see how this principle applies to real-world situations, from engines to refrigerators. It's key to understanding how energy behaves in physical and chemical processes.

Energy, Heat, and Work

Defining Energy, Heat, and Work

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• Energy is the capacity to do work or transfer heat and can be classified into various forms (kinetic, potential, thermal, chemical, and electrical energy)
• Heat is a form of energy transfer that occurs due to a temperature difference between two systems or within a system, always flowing from a higher temperature region to a lower temperature region
  • Example: Heat transfer occurs when a hot cup of coffee is placed in a cooler room, with heat flowing from the coffee to the surrounding air
• Work is the energy transfer that occurs when a force acts on an object, causing it to move in the direction of the force
  • In thermodynamics, work is often associated with the expansion or compression of a gas
  • Example: Work is done by a gas when it expands and pushes a piston in an engine

Differentiating Between Heat and Work

• The key difference between heat and work is that heat is a form of energy transfer that depends on temperature differences, while work is a form of energy transfer that depends on the application of a force over a distance
  • Heat transfer occurs spontaneously due to temperature gradients, without requiring an external force
  • Work requires the application of a force to an object, causing it to move in the direction of the force
• Example: In a refrigerator, heat is transferred from the cold interior to the warmer exterior through the use of a compressor (work), which applies a force to the refrigerant, causing it to move and transfer heat

Heat, Work, and Internal Energy

Internal Energy and Its Changes

• The internal energy of a system is the sum of the kinetic and potential energies of its constituent particles
  • It is a state function, meaning its value depends only on the current state of the system and not on the path taken to reach that state
• Changes in the internal energy of a system can occur due to heat transfer, work done by or on the system, or a combination of both
  • Example: When a gas is compressed (work done on the system), its internal energy increases due to the increased kinetic energy of the gas molecules
  • Example: When heat is added to a system, such as a pot of water on a stove, the internal energy of the water increases, leading to a rise in temperature

The First Law of Thermodynamics

• The relationship between heat, work, and internal energy changes is described by the first law of thermodynamics
  • The first law states that the change in internal energy of a system is equal to the sum of the heat added to the system and the work done on the system
  • Mathematically, this relationship is expressed as $ΔU = Q + W$, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done on the system
• If heat is removed from the system or work is done by the system, the corresponding terms in the equation will be negative
  • Example: When a gas expands and does work (W < 0), and no heat is added (Q = 0), the internal energy of the system decreases (ΔU < 0)

First Law of Thermodynamics

Applying the First Law of Thermodynamics

• The first law of thermodynamics is a powerful tool for analyzing energy changes in thermodynamic processes, allowing for the calculation of heat, work, or internal energy changes when the other two quantities are known
• When applying the first law, it is essential to:
  • Define the system and its boundaries clearly
  • Establish sign conventions for heat and work (typically, heat added to the system and work done on the system are considered positive, while heat removed from the system and work done by the system are considered negative)
• In many cases, the work done by or on the system can be calculated using the equation [W = -PΔV](https://www.fiveableKeyTerm:w_=_-pδv), where P is the pressure and ΔV is the change in volume
  • This equation is applicable to systems where the pressure remains constant during the process, such as in isobaric processes

Problem-Solving with the First Law

• When solving problems using the first law, it is crucial to identify the initial and final states of the system, as well as any relevant thermodynamic variables (temperature, pressure, and volume)
• Example: Consider a gas that expands isobarically from an initial volume of 2 L to a final volume of 4 L at a constant pressure of 1 atm. If 500 J of heat is added to the system during this process, calculate the change in internal energy.
  • Given: $V_1 = 2 L$, $V_2 = 4 L$, $P = 1 atm$, $Q = 500 J$
  • Step 1: Calculate the work done by the gas using $W = -PΔV$
    • $W = -(1 atm)(4 L - 2 L) = -2 L \cdot atm$
    • Convert units: $1 L \cdot atm = 101.325 J$, so $W = -202.65 J$
  • Step 2: Apply the first law of thermodynamics, $ΔU = Q + W$
    • $ΔU = 500 J + (-202.65 J) = 297.35 J$
  • Therefore, the change in internal energy of the gas during the isobaric expansion is 297.35 J.

Energy Transformations in Thermodynamic Processes

Isothermal and Adiabatic Processes

• Isothermal processes occur at constant temperature, and the internal energy of the system remains constant ($ΔU = 0$)
  • In an isothermal expansion or compression, the heat added to or removed from the system is equal to the work done by or on the system ($Q = -W$)
  • Example: In an isothermal expansion of an ideal gas, the gas does work ($W < 0$), and an equal amount of heat is added to the system ($Q > 0$) to maintain a constant temperature
• Adiabatic processes occur without any heat transfer between the system and its surroundings ($Q = 0$)
  • In an adiabatic process, the change in internal energy is equal to the work done by or on the system ($ΔU = W$)
  • In an adiabatic expansion, the system does work, and its internal energy decreases, resulting in a decrease in temperature
  • In an adiabatic compression, work is done on the system, and its internal energy increases, resulting in an increase in temperature
  • Example: In an adiabatic expansion of a gas, such as the expansion of a gas in a rapidly moving piston, no heat is exchanged with the surroundings, and the temperature of the gas decreases as it does work

Isobaric and Other Thermodynamic Processes

• Isobaric processes occur at constant pressure, and the heat added to or removed from the system is used to change both the internal energy and the work done by or on the system ($Q = ΔU + W$)
  • In an isobaric expansion, the system does work, and heat is added to maintain a constant temperature
  • In an isobaric compression, work is done on the system, and heat is removed to maintain a constant temperature
  • Example: In an isobaric heating process, such as heating a gas in a cylinder with a movable piston, heat is added to the gas, increasing its internal energy and causing it to expand and do work
• Other thermodynamic processes, such as isochoric (constant volume) and isentropic (constant entropy) processes, involve different energy transformations and relationships between heat, work, and internal energy changes
  • In an isochoric process, no work is done ($W = 0$), and any heat added or removed changes only the internal energy ($Q = ΔU$)
  • In an isentropic process, the process is both adiabatic and reversible, and the entropy of the system remains constant