Heat is the energy transfer due to the difference in temperature. Heat is a form of energy which the system can exchange with the surroundings if they are at different temperatures. The heat flows from higher temperature to lower temperature.

Heat is expressed as 'q'

Heat absorbed by the system = +q

Heat evolved by the system = - q

Work

It is the energy transfer due to the difference in pressure that is, the mode of energy transfer.

Types of work

(i) Mechanical Work (Pressure volume work) = Force x Displacement

(ii) Electrical Work = Potential difference x charge flow , VQ = EnF

(iii) $\mathrm{Expansion\ Work = P \times \Delta V = - P_{ext. } [ V _2-V _1] }$

$\textrm{P = external pressure And } \Delta \textrm{ V = increase or decrease in volume.}$

(iv) Gravitational Work = mgh

Here m = mass of body,

g = acceleration due to gravity

h = height moved.

Units: dyne cm or erg (C.G.S.)

Newton meter (joule)

(i) If the gas expands, [V₂> V₁] and work is done by the system and W is negative.

(ii) If the gas [V₂ < V₁] and work is done on the system and W is positive.

Different Types of Works and the Formulas

(i) Work done in reversible isothermal process

$\begin{array}{l}{\mathrm{W}=-2.303 \mathrm{nRT} \log _{10} \frac{\mathrm{V}_{2}}{\mathrm{V}_{1}}} \\ {\mathrm{W}=-2.303 \mathrm{nRT} \log _{10} \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}}}\end{array}$

(ii) Work done in irreversible isothermal process

$\\ \mathrm{ Work =- P_{ext. } ( V _2-V _1 )} \\ \mathrm{That \ is, \ Work =- P \times \Delta V }$

Internal Energy

Internal Energy or Intrinsic Energy

The energy stored within a substance is called its internal energy. The absolute value of internal energy cannot be determined.

It is the total energy of a substance depending upon its chemical nature, temperature, pressure, and volume, amount of substrate. It does not depend upon path in which the final state is achieved.

$\begin{array}{l}{\mathrm{E}=\mathrm{E}_{\mathrm{t}}+\mathrm{E}_{\mathrm{r}}+\mathrm{E}_{\mathrm{v}}+\mathrm{E}_{\mathrm{e}}+\mathrm{E}_{\mathrm{n}}+\mathrm{E}_{\mathrm{PE}}+\mathrm{E}_{\mathrm{B}}} \\ {\mathrm{E}_{\mathrm{t}}=\text { Transitional energy }} \\ {\mathrm{E}_{\mathrm{r}}=\text { Rotational energy }} \\ {\mathrm{E}_{\mathrm{PE}}=\text { Potential energy }} \\ {\mathrm{E}_{\mathrm{B}}=\text { Bond energy }}\end{array}$

The exact measurement of it is not possible so it is determined as $\mathrm {\Delta E}$ as follows:

$\\ \Delta \mathrm{E}=\Sigma \mathrm{E}_{\mathrm{p}}-\Sigma \mathrm{E}_{\mathrm{R}} \\ {\Delta \mathrm{E}=\mathrm{E}_{\mathrm{f}}-\mathrm{E}_{\mathrm{i}}} \\ {\text {Here } \mathrm{E}_{\mathrm{f}}=\text { final internal energy }} \\ {\mathrm{Ei}=\text { Initial internal energy }} \\ {\mathrm{Ep}=\text { Internal energy of products }} \\ {\mathrm{Er}=\text { Internal energy of reactants }}$

Facts about Internal Energy

It is an extensive property.
Internal energy is a state property.
The change in internal energy does not depend on the path by which the final state is reached.
Internal energy for an ideal gas a function of temperature only so when the temperature is kept constant $\mathrm{\Delta E}$ is zero for an ideal gas.

$\\\mathrm{E\propto T} \\ \\\mathrm{\Delta E = nC_v\Delta T [\ C_v \textup{ is the heat capacity at constant volume}]}$

For a cyclic process is zero $\Delta \mathrm{E}$ (E = state function), $\mathrm { E \propto T}$
For an ideal gas it is totally kinetic energy as there is no molecular interaction.
Internal energy for an ideal gas is a function of temperature only hence, when the temperature is kept constant it is zero.
At constant volume (Isochoric) $\mathrm {Q_v= \Delta E}$
For exothermic process, $\mathrm{\Delta E}$ is negative as but For endothermic process $\mathrm{\Delta E}$ is positive as .
It is determined by using a Bomb calorimeter. of the system.

$\begin{array}{l}{\Delta \mathrm{E}=\frac{\mathrm{Z} \times \Delta \mathrm{T} \times \mathrm{m}}{\mathrm{W}}} \\ {\mathrm{Z}=\text { Heat capacity of Bomb calorimeter }} \\ {\Delta \mathrm{T}=\text { Rise in temperature }} \\ {\mathrm{w}=\text { Weight of substrate (amount) }} \\ {\mathrm{m}=\text { Molar mass of substrate }}\end{array}$