A power plant burns natural gas to generate $740MW$ of electricity with $42\%$ efficiency. $88\%$ of the waste heat is removed by cooling water. The natural gas has a heat content of $49,000k\frac{J}{k}g.$

a$.$ How many tons of natural gas does this plant burn per day?

b$.$ Suppose the cooling water is taken from and returned to a river with a flow of $18\frac{m^3}{s}$ and an upstream temperature of $16C.$ What is the river temperature downstream of the power plant?

c$.$ Alternatively, the heat removed by cooling water can be removed by evaporating water rather than returning it to the river. If water is vaporized at a temperature of $50C,$ calculate the volumetric rate of loss of water to the atmosphere, in $\frac{m^3}{s},$ needed to cool the plant. Find and use constants appropriate to this temperature.