Heat, Temperature and Internal Energy — Revision Notes

⚡ 30-Second Revision

Temperature ($T$): — Measure of average molecular KE. SI unit: Kelvin (K). $T_K = T_C + 273.15$.
Heat ($Q$): — Energy in transit due to $Delta T$. Path function. SI unit: Joule (J). $1,cal approx 4.184,J$.
Internal Energy ($U$): — Total microscopic energy (KE + PE) of molecules. State function. SI unit: Joule (J).
Specific Heat Capacity ($c$): — Heat for $1,\text{kg}$ to change $1,\text{K}$. $Q = mcDelta T$.
Latent Heat ($L$): — Heat for $1,\text{kg}$ to change phase at constant $T$. $Q = mL$.
Ideal Gas Internal Energy: — $U propto T$. For monatomic: $U = \frac{3}{2}nRT$. For diatomic (moderate T): $U = \frac{5}{2}nRT$.
First Law of Thermodynamics: — $Delta U = Q - W$ (where $W$ is work done by system).

2-Minute Revision

Heat, temperature, and internal energy are foundational to thermodynamics. Temperature quantifies hotness/coldness, directly reflecting the average kinetic energy of a substance's particles. It's a state function, measured in Kelvin (K) for scientific accuracy.

Heat is energy transferred between systems due to a temperature difference, always flowing from hot to cold. It's a path function, measured in Joules (J). A substance doesn't 'contain' heat, but transfers it.

Internal energy is the total energy stored within a system's molecules, including their kinetic and potential energies. It's a state function, also measured in Joules. For an ideal gas, internal energy depends solely on absolute temperature.

Key formulas include $Q = mcDelta T$ for temperature changes and $Q = mL$ for phase changes. The First Law of Thermodynamics, $Delta U = Q - W$, links these concepts, stating that internal energy changes due to heat added and work done.

5-Minute Revision

To master Heat, Temperature, and Internal Energy for NEET, focus on their precise definitions and interrelationships. **Temperature ($T$)** is the macroscopic manifestation of the average translational kinetic energy of molecules.

Remember the Kelvin scale ($T_K = T_C + 273.15$) is crucial for absolute temperature calculations. **Heat ($Q$)** is the energy transfer mechanism driven by temperature differences, always from higher to lower temperature.

It's a 'path function,' meaning the amount of heat transferred depends on the process. Its SI unit is the Joule. Key calculations involve specific heat capacity ($c$) for temperature changes ($Q = mcDelta T$) and latent heat ($L$) for phase changes at constant temperature ($Q = mL$).

For example, melting $1,\text{kg}$ of ice at $0^circ C$ requires $Q = (1,\text{kg}) \times L_f$, where $L_f$ is latent heat of fusion. **Internal Energy ($U$)** is the total microscopic energy (kinetic and potential) stored within a system.

It's a 'state function,' depending only on the system's current state (e.g., $T, P, V$). For an ideal gas, $U$ depends only on $T$ ($U = \frac{f}{2}nRT$). The First Law of Thermodynamics ($Delta U = Q - W$) is central, showing how internal energy changes with heat added ($Q$) and work done by the system ($W$).

Always pay attention to signs: $Q$ is positive when heat is added to the system, $W$ is positive when work is done *by* the system. Distinguish these terms clearly to avoid common conceptual pitfalls.

Prelims Revision Notes

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**Temperature ($T$):**

* Definition: Measure of average translational kinetic energy of molecules. * Units: Kelvin (K) is SI, Celsius ($^circ C$), Fahrenheit ($^circ F$). * Conversion: $T_K = T_C + 273.15$. $Delta T_C = Delta T_K$. * Absolute Zero: $0,\text{K}$ ($-273.15^circ C$), theoretical point of zero molecular motion. * Thermal Equilibrium: No net heat flow between objects at the same temperature (Zeroth Law).

1
**Heat ($Q$):**

* Definition: Energy transferred due to temperature difference. * Nature: Energy in transit, a path function (depends on process). * Units: Joule (J) is SI, calorie (cal). $1,cal approx 4.184,J$. * Flow: Always from higher temperature to lower temperature.

* **Specific Heat Capacity ($c$):** Heat required to change $1,\text{kg}$ of substance by $1,\text{K}$. * Formula: $Q = mcDelta T$. * Units: $J/(kg cdot K)$ or $J/(kg cdot ^circ C)$. * **Latent Heat ($L$):** Heat required for phase change of $1,\text{kg}$ at constant temperature.

* Formula: $Q = mL$. * Units: $J/kg$. * Types: Latent heat of fusion ($L_f$) for solid-liquid, Latent heat of vaporization ($L_v$) for liquid-gas.

1
**Internal Energy ($U$):**

* Definition: Total microscopic energy of a system (sum of molecular KE and PE). * Nature: Property of the system, a state function (depends only on state, not path). * Units: Joule (J). * Components: Translational, rotational, vibrational KE; intermolecular PE.

* For Ideal Gas: * Intermolecular PE is negligible. * Depends ONLY on absolute temperature ($U propto T$). * Monatomic gas ($f=3$): $U = \frac{3}{2}nRT$. * Diatomic gas ($f=5$ at moderate T): $U = \frac{5}{2}nRT$.

* Polyatomic gas ($f=6$ at moderate T): $U = \frac{6}{2}nRT = 3nRT$. * First Law of Thermodynamics: $Delta U = Q - W$ (where $W$ is work done *by* the system). * $Q > 0$: Heat added to system. * $Q < 0$: Heat removed from system.

* $W > 0$: Work done *by* system. * $W < 0$: Work done *on* system.

Key Distinctions:

Heat is transfer, Internal Energy is stored. Temperature is a measure.
Heat is path function, Internal Energy and Temperature are state functions.
Always use Kelvin for absolute temperature in gas laws and internal energy calculations.

Vyyuha Quick Recall

To remember the key differences: Hot Tea Is Energy.

Hot: Heat is Hotness transfer.
Tea: Temperature is Thermal intensity (average KE).
Is: Internal energy Is stored energy (total KE + PE).
Energy: All are related to Energy.