Thermal Equilibrium — Revision Notes

⚡ 30-Second Revision

Thermal Equilibrium: — State of no net heat transfer; uniform temperature.
Zeroth Law: — If $A \leftrightarrow C$ and $B \leftrightarrow C$, then $A \leftrightarrow B$.
Temperature (T): — Measure of average molecular kinetic energy; intensive property.
Heat (Q): — Energy in transit due to $\Delta T$; extensive property.
Heat Flow Direction: — Hotter $\rightarrow$ Colder.
Calorimetry Principle: — Heat Lost = Heat Gained ($m_1 c_1 \Delta T_1 = m_2 c_2 \Delta T_2$).
Mechanisms: — Conduction, Convection, Radiation (all lead to equilibrium).
Internal Energy (U): — Total energy of molecules; extensive property (not necessarily equal at equilibrium).

2-Minute Revision

Thermal equilibrium is the state where two or more systems in thermal contact have reached a uniform temperature, resulting in no net exchange of heat energy. This fundamental concept is formalized by the Zeroth Law of Thermodynamics: if system A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with system C, then A and B are in thermal equilibrium with each other.

This law provides the basis for temperature measurement using thermometers. Temperature is an intensive property, a measure of the average kinetic energy of molecules, while heat is the energy transferred due to a temperature difference.

Heat always flows from a region of higher temperature to lower temperature until equilibrium is established. This process can occur via conduction, convection, or radiation. It's crucial to remember that at thermal equilibrium, while temperatures are equal and net heat flow is zero, the internal energies of the systems are not necessarily equal, as internal energy is an extensive property dependent on mass and specific heat.

5-Minute Revision

Thermal equilibrium is a critical concept in thermodynamics, signifying a state where systems in thermal contact cease to have any net transfer of heat energy between them. This occurs when all interacting components achieve a uniform temperature.

The underlying principle is that heat, defined as the transfer of thermal energy driven by a temperature difference, will spontaneously flow from a hotter region to a colder region. This flow continues until the temperature gradient is eliminated, and the systems reach a common final temperature.

The Zeroth Law of Thermodynamics is the formal statement that underpins this concept and the very definition of temperature. It states: 'If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.' This law is vital because it enables the consistent measurement of temperature using a thermometer (the third system), allowing us to compare the 'hotness' or 'coldness' of different objects indirectly.

Key distinctions to remember for NEET are between heat, temperature, and internal energy. Temperature is an intensive property, reflecting the average kinetic energy of particles. Heat is energy in transit. Internal energy is an extensive property, representing the total energy of all particles. At thermal equilibrium, temperatures are equal, and the average kinetic energy of molecules is the same, but total internal energies may differ if masses or specific heats vary.

Heat transfer mechanisms—conduction, convection, and radiation—are the processes through which systems move towards thermal equilibrium. Conduction involves direct particle-to-particle energy transfer, convection involves fluid movement, and radiation involves electromagnetic waves. All these mechanisms work to equalize temperatures.

Worked Mini-Example (Calorimetry):

A $0.5,\text{kg}$ metal block (specific heat $c_m = 400,\text{J/kg}\cdot\text{K}$) at $80^{\circ}\text{C}$ is dropped into $1,\text{kg}$ of water (specific heat $c_w = 4200,\text{J/kg}\cdot\text{K}$) at $20^{\circ}\text{C}$. Assuming an insulated container, find the final equilibrium temperature ($T_f$).

Approach: Apply the principle of calorimetry: Heat lost by metal = Heat gained by water.

Solution:

$m_m c_m (T_{m,i} - T_f) = m_w c_w (T_f - T_{w,i})$ $(0.5,\text{kg})(400,\text{J/kg}\cdot\text{K})(80^{\circ}\text{C} - T_f) = (1,\text{kg})(4200,\text{J/kg}\cdot\text{K})(T_f - 20^{\circ}\text{C})$ $200(80 - T_f) = 4200(T_f - 20)$ $16000 - 200T_f = 4200T_f - 84000$ $16000 + 84000 = 4200T_f + 200T_f$ $100000 = 4400T_f$ $T_f = \frac{100000}{4400} \approx 22.73^{\circ}\text{C}$

The final equilibrium temperature is approximately $22.73^{\circ}\text{C}$, which is between the initial temperatures of $20^{\circ}\text{C}$ and $80^{\circ}\text{C}$.

Prelims Revision Notes

Thermal equilibrium is a state where there is no net heat transfer between systems in thermal contact, meaning they have reached a uniform temperature. This is a crucial concept for NEET Physics.

Key Definitions & Laws:

Thermal Equilibrium: — $T_A = T_B$ for systems A and B in contact, implying $Q_{net} = 0$.
Zeroth Law of Thermodynamics: — If $T_A = T_C$ and $T_B = T_C$, then $T_A = T_B$. This law defines temperature and is the basis for thermometry.
Temperature (T): — An intensive property, directly proportional to the average translational kinetic energy of molecules ($E_{avg} \propto T$). Measured in Celsius ($^{\circ}\text{C}$) or Kelvin (K). For calculations, use Kelvin for absolute values, but $\Delta T$ is the same in $^{\circ}\text{C}$ and K.
Heat (Q): — Energy transferred due to a temperature difference. It is an extensive property and is measured in Joules (J) or calories (cal). $1\,\text{cal} = 4.186\,\text{J}$.
Internal Energy (U): — The total energy (kinetic + potential) of the molecules within a system. It is an extensive property. At thermal equilibrium, temperatures are equal, but internal energies are not necessarily equal.

Heat Transfer Mechanisms:

These are the ways systems reach thermal equilibrium:

1
Conduction: — Direct transfer through molecular collisions (solids).
2
Convection: — Transfer through bulk movement of fluids (liquids, gases).
3
Radiation: — Transfer via electromagnetic waves (does not require a medium, e.g., in vacuum).

Calorimetry Principle (Conservation of Energy):

For an isolated system, when substances at different temperatures are mixed, the heat lost by the hotter substance(s) equals the heat gained by the colder substance(s).

Heat lost = Heat gained
$m_1 c_1 (T_{initial,1} - T_{final}) = m_2 c_2 (T_{final} - T_{initial,2})$

* $m$: mass * $c$: specific heat capacity * $T_{initial}$: initial temperature * $T_{final}$: final equilibrium temperature

Common Mistakes to Avoid:

Confusing heat and temperature.
Assuming internal energies are equal at thermal equilibrium.
Incorrectly applying the direction of heat flow (always hot to cold).
Forgetting that radiation occurs in a vacuum.
Not converting units consistently (e.g., specific heat in J/kg\cdotK and mass in grams).

Focus on conceptual clarity and practice calorimetry problems thoroughly, including those involving phase changes, as they are frequently tested.

Vyyuha Quick Recall

Thermal Equilibrium Zero Heat Transfer In Contact.

Thermal Equilibrium: The state.
Zero Heat Transfer: What happens at equilibrium (net).
In Contact: Condition for heat exchange.

Also, Zeroth Law Tells Temperature: The Zeroth Law defines temperature and is the basis for thermometry.