Key Points

Heat is the form of energy transferred between systems due to a temperature difference, measured in Joules (J). Temperature is a measure of the degree of hotness or coldness of a body, with the SI unit Kelvin (K).

Heat is the form of energy transferred between systems due to a temperature difference, measured in Joules (J). Temperature is a measure of the degree of hotness or coldness of a body, with the SI unit being Kelvin (K).

The Celsius ($t_C$), Fahrenheit ($t_F$), and Kelvin (T) scales are inter-related. The key conversion formulas are $t_F = (\frac{9}{5})t_C + 32$ and $T = t_C + 273.15$.

The Celsius ($t_C$) and Fahrenheit ($t_F$) scales are related by the formula $t_F = (\frac{9}{5})t_C + 32$. The Kelvin (T) and Celsius scales are related by $T = t_C + 273.15$.

The ideal gas equation describes the state of a hypothetical ideal gas, relating pressure (P), volume (V), and absolute temperature (T). The equation is $PV = \mu RT$, where $\mu$ is the number of moles and R is the universal gas constant.

The ideal gas equation is $PV = \mu RT$, where P is pressure, V is volume, T is absolute temperature, $\mu$ is the number of moles, and R is the universal gas constant. Absolute zero (0 K or $-273.15^{\circ}\text{C}$) is the temperature at which an ideal gas would have zero pressure.

The increase in length of a solid due to a temperature change is called linear expansion. The change in length ($\Delta l$) is given by $\Delta l = l_0 \alpha_l \Delta T$, where $l_0$ is the original length and $\alpha_l$ is the coefficient of linear expansion.

Absolute zero (0 K or $-273.15^{\circ} \text{C}$) is the theoretical temperature at which all molecular motion ceases. The Kelvin scale is an absolute temperature scale starting from this point.

When a solid is heated, its length increases. The fractional change in length ($\frac{\Delta l}{l}$) is directly proportional to the change in temperature ($\Delta T$), given by $\frac{\Delta l}{l} = \alpha_l \Delta T$, where $\alpha_l$ is the coefficient of linear expansion.

The increase in volume of a substance due to a temperature change is called volume expansion. The change in volume ($\Delta V$) is given by $\Delta V = V_0 \alpha_V \Delta T$, where $V_0$ is the original volume and $\alpha_V$ is the coefficient of volume expansion.

For an isotropic solid, the coefficient of volume expansion ($\alpha_V$) is approximately three times the coefficient of linear expansion ($\alpha_l$). The relationship is $\alpha_V = 3\alpha_l$.

Similar to linear expansion, area and volume also increase with temperature. The coefficient of volume expansion ($\alpha_V$) is related to the linear expansion coefficient by $\alpha_V = 3\alpha_l$ for isotropic solids.

Water exhibits an anomalous behavior where it contracts upon heating from $0^{\circ} \text{C}$ to $4^{\circ} \text{C}$. This means water has its maximum density at $4^{\circ} \text{C}$, which has important environmental effects.

Water exhibits anomalous behavior, contracting on heating from $0^{\circ}\text{C}$ to $4^{\circ}\text{C}$. It has its maximum density at $4^{\circ}\text{C}$, which is why lakes freeze from the top down.

Specific heat capacity (s) is the amount of heat required to raise the temperature of a unit mass of a substance by one degree. The formula is $\Delta Q = ms\Delta T$, where m is mass and $\Delta Q$ is the heat supplied.

Specific heat capacity (s) is the amount of heat required to raise the temperature of a unit mass of a substance by one degree. The formula is $s = \frac{1}{m} \frac{\Delta Q}{\Delta T}$, with SI units of $\text{J kg}^{-1} \text{K}^{-1}$.

Molar specific heat capacity (C) is the heat required per mole to raise the temperature by one degree. For gases, it is defined at constant volume ($C_V$) or constant pressure ($C_P$).

Calorimetry operates on the principle of energy conservation in an isolated system. When bodies at different temperatures are mixed, the heat lost by the hotter body is equal to the heat gained by the colder body.

A change of state (e.g., melting, boiling) occurs at a constant temperature. The heat required for this change is called latent heat (L), calculated by $Q = mL$, where m is the mass.

In an isolated system, the heat lost by a hotter body is equal to the heat gained by a colder body until they reach thermal equilibrium. This principle is expressed as Heat Lost = Heat Gained.

During a change of state (e.g., melting or boiling), the temperature of the substance remains constant. The heat required for this phase change is called latent heat (L), given by the formula $Q = mL$.

Latent heat of fusion ($L_f$) is the heat per unit mass to change a substance from solid to liquid. Latent heat of vaporization ($L_v$) is the heat per unit mass to change a substance from liquid to gas.

The triple point is the specific temperature and pressure at which the solid, liquid, and gas phases of a substance can coexist in thermal equilibrium. For water, this occurs at 273.16 K.

Latent heat of fusion ($L_f$) is the heat per unit mass required to change a substance from solid to liquid. Latent heat of vaporization ($L_v$) is the heat per unit mass required to change a substance from liquid to gas.

Heat can be transferred in three ways: conduction (through direct contact), convection (through the movement of fluids), and radiation (through electromagnetic waves).

Conduction is the transfer of heat through a material without any bulk movement of the material itself. The rate of heat flow is given by $H = KA \frac{T_C - T_D}{L}$, where K is the thermal conductivity.

The rate of heat flow (H) through a material is given by $H = KA \frac{T_C - T_D}{L}$, where K is the thermal conductivity, A is the cross-sectional area, L is the length, and $(T_C - T_D)$ is the temperature difference.

Convection is the mode of heat transfer by the actual motion of matter, which occurs only in fluids (liquids and gases). It is responsible for phenomena like sea breezes and wind patterns.

Radiation is the transfer of heat in the form of electromagnetic waves, which can travel through a vacuum. This is how the Earth receives heat from the Sun.

All objects with a temperature above absolute zero emit thermal radiation. The rate of energy radiated (H) is given by the Stefan-Boltzmann law: $H = A e \sigma T^4$, where A is the surface area, e is emissivity, and $\sigma$ is the Stefan-Boltzmann constant.

This law states that the total radiant heat energy emitted from a surface is proportional to the fourth power of its absolute temperature. The formula is $H = A e \sigma T^4$, where $\sigma$ is the Stefan-Boltzmann constant.

Wien's displacement law states that the wavelength of maximum emission ($\lambda_m$) from a blackbody is inversely proportional to its absolute temperature (T). The formula is $\lambda_m T = \text{constant}$.

For a small temperature difference between a body and its surroundings, the rate of loss of heat from the body is directly proportional to the temperature difference. The law is expressed as $\frac{dQ}{dt} = -k(T_2 - T_1)$.

Wien's law relates the temperature of a blackbody to the wavelength at which it emits the most light. It states that $\lambda_m T = \text{constant}$, where $\lambda_m$ is the peak wavelength.

This law states that the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings, provided the temperature difference is small.