Ideal Gas

• 1). Determine whether the gas is an ideal static gas or an ideal diatomic gas. Ideal static gases are theoretical and do not exist in nature. Diatomic gases have two gas atoms in their molecules. The molecular state of the gas will be mentioned in the problem.
  
  
• 2). Calculate density of the gas (n), average speed of the gas (<c>), mean free path of the gas particles (l), specific heat capacity of the gas (c_v). These values are constant for a gas at a given temperature but vary for different gases. These values can be found in any science handbook that lists scientific constants.
  
  
• 3). Substitute the values in the equation K = n*<c>*l*c_v/3. K gives the thermal conductivity of the gas. The unit for K is given by [J/(cm*s*deg)]
  
  

Diatomic Gas

• 1). Calculate the average speed of the the diatomic gas using the formula <c>(T) = (8*R*T/pi*M)^1/2. This formula is derived from kinetic theory of gases. Average speed of the gas is used because the gas molecules have different speeds at the same temperature. Average speed for a gas varies with temperature.
  
  Here R is the gas constant, T is the absolute temperature, and M is the molar mass of the gas. If the temperature (T) is given in Celsius or Fahrenheit scale, convert it to Kelvin or Rankine scale to get absolute temperature. The gas constant (R) is a universal constant.
  
  
• 2). Substitute the value of the average speed of diatomic gas from the previous step and the value of constant-volume heat capacity using the formula c_v = 5/2*R in the formula K = n*<c>*l*c_v/3.
  
  In certain cases constant-volume heat capacity is expressed in terms of internal energy. In these cases, constant-volume heat capacity is calculated as the the partial derivative of internal energy with respect to temperature at constant specific volume.
  R is the gas constant.
  
  
• 3). Use the formula K(T) = 5/3 * n * l * {(2* R^2 * T)/(pi * M)}^1/2 to derive thermal conductivity of the gas. This expresses thermal conductivity in terms of temperature. This formula is a simplification of the above two steps.