Heat Reservoir

Definition

A heat reservoir (also known as a thermal reservoir) is a thermodynamic system with a sufficiently large heat capacity such that any amount of heat transferred to or from it does not change its temperature. It acts as an infinite source or sink of thermal energy, maintaining a constant temperature regardless of the process occurring in the system connected to it.

Main Content

1. Thermal Equilibrium and Capacity

• A reservoir must possess a massive heat capacity, meaning it can absorb or release large quantities of energy without experiencing a measurable change in temperature ($T = \text{constant}$).
• Because the temperature remains constant, heat exchange with a reservoir is considered a reversible process in the context of ideal thermodynamic cycles.

2. Source vs. Sink

• A Heat Source is a reservoir at a high temperature that supplies thermal energy to a system (e.g., a boiler in a power plant).
• A Heat Sink is a reservoir at a low temperature that absorbs waste heat from a system (e.g., the atmosphere or a cold river).

3. Thermodynamic Representation

• In theoretical physics, we represent the reservoir as a body where $\Delta T \approx 0$ even if $Q$ (heat) is added or removed.
• This simplification allows us to calculate efficiency in engines like the Carnot engine without accounting for the internal state changes of the external environment.

       [ System ]
      /          \
  (Q_in)        (Q_out)
    |              |
[ Source ]      [ Sink ]
(T_high)        (T_low)

Working / Process

1. Energy Extraction (From Source)

• The system interacts with the high-temperature reservoir.
• Thermal energy flows spontaneously from the hot reservoir into the system because the system's internal temperature is lower than that of the reservoir.

2. Work Conversion

• The system uses the absorbed energy to perform mechanical work (expansion).
• During this phase, the reservoir provides energy without dropping its own temperature, effectively keeping the input constant.

3. Heat Rejection (To Sink)

• The system expels remaining waste heat into the low-temperature reservoir (the sink).
• The sink accepts this energy without increasing its temperature, allowing the cycle to reset to its original state.

Advantages / Applications

• Efficiency Calculation: Provides the baseline for calculating the maximum theoretical efficiency of heat engines (Carnot Efficiency).
• Climate Control: Large bodies of water (like oceans) act as reservoirs, stabilizing the Earth's temperature by absorbing excess atmospheric heat.
• Industrial Processing: Industrial cooling systems use large water tanks as heat sinks to maintain stable operating temperatures for machinery.

Summary

A heat reservoir is a conceptual or physical system with an infinite heat capacity that maintains a constant temperature regardless of heat transfer. It functions as either an energy source or an energy sink, essential for defining thermodynamic cycles and analyzing engine efficiency.

• Thermal Equilibrium: State where temperature remains constant.
• Heat Source: Provides energy ($T_{high}$).
• Heat Sink: Absorbs energy ($T_{low}$).
• Key Term: Infinite Heat Capacity.