# List of formulas related to Gas Laws

## Kelvin Temprerature

T: temperature in Kelvin scale, t: temperature in Celsius scale

T = toC + 273(K)

### Equation Of State

p: pressure(P, Pascal), V: volume(m3), n: number of moles of the gas(mol), R: universal gas constant, T: Kelvin temperature of the gas (K), k: Boltzmann’s constant, N: number of molecules in the gas.

pV = nRT = NkT

k = 1.38(24) X 10-23J/K

k = 8.617(15) X 10-5eV/K

R = 8.314J/mol.K

### Ideal Gas Law

$$\frac{p_1 V_1}{T_1} = \frac{p_2 V_2}{T_2}$$ $$\frac{p V}{T} = constant$$

### Boyle's Law For Pressure

If the temperature of the gas is constant

pV = constant

p1V1 = p2V2 = ....pnVn

### Gay-Lussac's Law Of Pressure-Temperature

If tha volume on a gas is constant

$$\frac{P}{T} = constant$$ $$\frac{P_1}{T_1} = \frac{P_2}{T_2} = ..... = \frac{P_n}{T_n}$$

P: pressure of gas at temperature t, po; pressure at 0 celsius, γ: factor when volume is constant

$$p = p_0 (1 + \gamma t)$$ $$= p_0( 1 + \frac{1}{273} t)$$ $$\text{Example when t=0 kelvin}$$ $$t = \frac{-1}{\gamma} = -273^o C$$ $$p = p_0( 1 + \gamma \frac{-1}{\gamma}) = 0$$

#### Charle's Law Of Volumes

If the pressure on a gas is constant

$$\frac{V}{T} = constant$$ $$\frac{V_1}{T_1} = \frac{V_2}{T_2} = ..... = \frac{V_n}{T_n}$$