Lime has many uses, including as a fluxing agent during steel-making. Lime is produced by thermal decomposing (calcining) of limestone via the following reaction: CaCO3CaO+CO2 Lime production is typically via the rotary kiln, a long, inclined, refractory-lined, steel shell rotating on trunnion wheels. Limestone is supplied at the high end and moves axially by the combined effects of gravity and rotation. As the material progresses along the kiln, its temperature increases by heat transfer from the hot gases produced by the burner located at the lime discharge end. In one operation, dry limestone is supplied at 25C and CaO exits at 1000C. Natural gas fuel (assume to be 100%CH4 ) is burned in 15% excess air (assume both start at 25C ). The off-gas leaves the kiln at 525C. Assume that the Cp expression for H2O is valid across the entire temperature range (you do not need to account for the heat of vaporization of water). If the energy loss from the process is 300,000kJ per 1000kg of lime, perform a complete mass and energy balance to determine the natural gas requirement and the volume and composition (in vol. \%) of the off-gas. You can assume 1000kg of lime as the basis for mass and energy balance equations