Calculate the number of kilograms of coal oil and natural ga

Calculate the number of kilograms of coal, oil, and natural gas that must be burned each day to operate a 3000-MW thermal power plant, which otherwise consumes 3.9 kg/d of uranium-235. The heats of combustion of the three fuels (in kJ/g) are, respectively, 32, 44, and 50.

Solution

Solution of the question can be done by equating the energy produced by uranium and energy produced by others

Energy produced by uranium-235 per day =m_u*Calorific value of uranium

;m_u = uranium consumed/day

= 3.9Kg/Day * 500000 MJ/kg =19.5 *10⁵MJ/day

Case 1 : Energy of coal produced per day = Energy of uranium-235 per day

m_c * calorific value of coal = 19.5 *10⁵MJ/day m_c = mass of coal used per day

m_c = (19.5 *10⁵)/25MJ/kg = 78000 kg/day   calorific value of coal (hard black) =25MJ/kg

So amount of coal required to run 3000MW power plant = 78000kg/day

Case 2 : Energy of oil produced per day = Energy of uranium-235 per day

m_o * calorific value of oil = 19.5 *10⁵MJ/day m_o = mass of oil used per day

m_o = (19.5 *10⁵)/45MJ/kg =43334 kg/day   calorific value of oil =45MJ/kg

So amount of oil required to run 3000MW power plant =43334 kg/day

Case 3 : Energy of natural gas produced per day = Energy of uranium-235 per day

m_n * calorific value of natural gas = 19.5 *10⁵MJ/day   m_n = volume of natural gas used per day

m_n = (19.5 *10⁵)/38MJ/m³= 51315 m³/day   calorific value of natural gas =MJ/m³

So amount of natural gas required to run 3000MW power plant = 51315 m³/day