Madhyamik Physical Science – Important Formula
1. Behavior of Gases
Boyle's Law
$$P_1V_1 = P_2V_2$$Charles's Law
$$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$Temperature Conversion
$$T = t + 273$$Combined Gas Law
$$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$Ideal Gas Equation
$$PV = nRT$$or
$$PV = \frac{W}{M}RT$$Number of Moles
$$n = \frac{W}{M}$$or
$$n = \frac{N}{N_A}$$Molecular Mass from Density
$$M = \frac{dRT}{P}$$2. Light
Relation between Focal Length and Radius
$$f = \frac{r}{2}$$Snell's Law
$$\mu = \frac{\sin i}{\sin r}$$Refractive Index and Velocity
$$\mu = \frac{c}{v}$$Angle of Deviation in Prism
$$\delta = (i_1 + i_2) - A$$Linear Magnification
$$m = \frac{v}{u}$$or
$$m = \frac{\text{Height of Image}}{\text{Height of Object}}$$Power of Lens
$$P = \frac{1}{f}$$or
$$P = \frac{100}{f}$$3. Periodic Table
If valency of element A = x and element B = y
$$A_yB_x$$Example:
$$Al^{3+} + O^{2-} \rightarrow Al_2O_3$$Important Constants
$$R = 0.0821 , L,atm,mol^{-1}K^{-1}$$ $$R = 8.314 , J,mol^{-1}K^{-1}$$
\documentclass{article} \usepackage{amsmath} \begin{document} \title{Madhyamik Physical Science: Important Mathematical Formulae} \date{} \maketitle \section{Behavior of Gases} \subsection{Boyle's Law} \[ P_1V_1 = P_2V_2 \] \subsection{Charles's Law} \[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \] Temperature conversion: \[ T = t^\circ C + 273 \] \subsection{Combined Gas Law} \[ \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \] \subsection{Ideal Gas Equation} \[ PV = nRT \] or \[ PV = \frac{W}{M}RT \] where \[ n = \frac{W}{M} \] \subsection{Number of Moles from Number of Particles} \[ n = \frac{N}{N_A} \] \subsection{Molecular Mass from Density} \[ M = \frac{dRT}{P} \] \section{Light} \subsection{Relation between Focal Length and Radius of Curvature} \[ f = \frac{r}{2} \] \subsection{Snell's Law} \[ \mu = \frac{\sin i}{\sin r} \] \subsection{Refractive Index and Velocity of Light} \[ \mu = \frac{c}{v} \] \subsection{Angle of Deviation in Prism} \[ \delta = (i_1 + i_2) - A \] \subsection{Linear Magnification} \[ m = \frac{v}{u} \] or \[ m = \frac{\text{Height of Image}}{\text{Height of Object}} \] \subsection{Power of Lens} \[ P = \frac{1}{f} \] or \[ P = \frac{100}{f} \] \section{Periodic Table} \subsection{Formation of Chemical Compound} If valency of element A = $x$ and element B = $y$ \[ \text{Compound Formula} = A_yB_x \] Example: \[ Al^{3+} + O^{2-} \rightarrow Al_2O_3 \] \section{Important Constants} Temperature conversion: \[ T = t + 273 \] Gas constant values: \[ R = 0.0821 \, L\,atm\,mol^{-1}K^{-1} \] \[ R = 8.314 \, J\,mol^{-1}K^{-1} \] \end{document}
