3.2 Work, Heat, and Internal Energy

Thermodynamics is all about energy and how it moves around. Work happens when things change size, like a gas expanding in a cylinder. Heat flows between objects at different temperatures. These processes can change a system's internal energy.

The first law of thermodynamics ties it all together. It says that energy can't be created or destroyed, just moved around. We use this to figure out how much work is done, heat is transferred, or internal energy changes in different situations.

Thermodynamic Processes and Energy

Work through volume changes

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• Work in thermodynamics is associated with volume changes in a system
  • Positive work is done by a system when it expands against an external pressure (piston moving outward in a cylinder)
  • Negative work is done on a system when an external pressure compresses the system (piston moving inward in a cylinder)
• The work done is equal to the external pressure multiplied by the change in volume
  • $W = -P \Delta V$, where $W$ is work, $P$ is external pressure, and $\Delta V$ is the change in volume
• The negative sign in the work equation accounts for the sign convention
  • When the system expands ($\Delta V > 0$), work is positive (done by the system)
  • When the system is compressed ($\Delta V < 0$), work is negative (done on the system)
• Examples:
  • A gas in a cylinder expanding and pushing a piston outward performs positive work
  • A gas in a cylinder being compressed by an external force (piston moving inward) experiences negative work
• Cyclic processes involve a series of thermodynamic states that eventually return the system to its initial state

Calculations for thermodynamic processes

• The first law of thermodynamics relates heat transfer ($Q$), work done ($W$), and the change in internal energy ($\Delta U$)
  • $\Delta U = Q + W$, where $\Delta U$ is the change in internal energy, $Q$ is heat transfer, and $W$ is work done
• Heat transfer ($Q$) is positive when heat is added to the system and negative when heat is removed from the system
  • Example: A system absorbing heat from its surroundings has positive $Q$
• Work done ($W$) is positive when work is done by the system (expansion) and negative when work is done on the system (compression)
  • Example: A gas expanding and lifting a weight performs positive work
• The change in internal energy ($\Delta U$) is the sum of heat transfer and work done
  • If $\Delta U > 0$, the internal energy of the system increases (system gains energy)
  • If $\Delta U < 0$, the internal energy of the system decreases (system loses energy)
• For an isothermal process (constant temperature), $\Delta U = 0$, so $Q = -W$
  • Example: An ideal gas expanding isothermally absorbs heat equal to the work it performs
• For an adiabatic process (no heat transfer), $Q = 0$, so $\Delta U = W$
  • Example: A gas expanding adiabatically in an insulated cylinder experiences a decrease in internal energy equal to the work done
• The specific heat capacity of a substance determines how much heat is required to change its temperature by a given amount

Temperature and internal energy

• The internal energy of an ideal gas depends only on its temperature
  • [object Object],[object Object], where $U$ is internal energy, $n$ is the number of moles, $R$ is the universal gas constant (8.314 J/mol·K), and $T$ is the absolute temperature (K)
• For an ideal gas, the change in internal energy ($\Delta U$) is directly proportional to the change in temperature ($\Delta T$)
  • $\Delta U = \frac{3}{2}nR\Delta T$
• If the temperature of an ideal gas increases ($\Delta T > 0$), its internal energy increases ($\Delta U > 0$)
  • Example: Heating a gas in a closed container increases its temperature and internal energy
• If the temperature of an ideal gas decreases ($\Delta T < 0$), its internal energy decreases ($\Delta U < 0$)
  • Example: Cooling a gas in a closed container decreases its temperature and internal energy
• For processes where the temperature remains constant (isothermal), the internal energy of an ideal gas does not change ($\Delta U = 0$)
  • Example: An ideal gas expanding isothermally maintains constant internal energy

Thermodynamic Systems and Processes

• Thermodynamic equilibrium is a state where all intensive properties of a system are uniform and not changing with time
• Entropy is a measure of the disorder or randomness in a system, which tends to increase in natural processes
• Heat engines are devices that convert thermal energy into mechanical work through cyclic processes