Develop equations that may be solved to give the final temperature of the gas remaining in a tank after the tank has been bled from an initial pressure P₁ to a final pressure P₂. Known quantities are initial temperature, tank volume, heat capacity of the gas, total heat capacity of the containing tank, P₁, and P₂. Assume the tank to be always at the temperature of the gas remaining in the tank and the tank to be perfectly insulated.