Charles law in terms of absolute temperature, gas equation in terms of density

Charles' Law:

Charles' Law states that the volume of a gas is directly proportional to its absolute temperature, provided that the pressure and the number of moles of gas are kept constant. 

This law can be expressed mathematically as:

V/T = k

where 

  • V is the volume of the gas, 
  • T is the absolute temperature (in Kelvin),
  • and k is a constant.

Gas Equation in terms of Density:

The Ideal Gas Law states that the pressure, volume, and temperature of an ideal gas are related by the equation:

PV = nRT, 

where 

  • P is the pressure, 
  • V is the volume, n is the number of moles of gas, 
  • R is the Universal Gas Constant, 
  • and T is the temperature in Kelvin.


By rearranging the Ideal Gas Law equation, we can obtain an expression for the density of a gas in terms of its pressure, temperature, and molar mass:

ρ = m/V = nM/V = PM/RT, 

where 

  • ρ is the density of the gas,
  •  m is the mass of the gas, 
  • M is the molar mass, and 
  • R and T are as defined above.


So, in terms of density, the Ideal Gas Law can be written as: ρ = PM/RT, where P is the pressure, T is the temperature in Kelvin, M is the molar mass, and R is the Universal Gas Constant.