Assume that for a domestic hot water supply, 200 kg of water per day must be heated from 15°C to 60°C and methane gas is used for this purpose. What volume of methane at STP (molar volume 22.4 l/mol)

Question

Assume that for a domestic hot water supply, 200 kg of water per day must be heated from 15°C to 60°C and methane gas is used for this purpose. What volume of methane at STP (molar volume 22.4 l/mol) would have to be used, with an efficiency of 50%? Heat of combustion of methane is -200 kcal/mol and specific heat capacity of water is 1.0 cal/K-g.

TestHub · Accepted Answer

Heat needed = 200000 g × 1.0 × 45 = 9.0 × 10 6 cal = 9000 kcal. At 50% efficiency, heat to be supplied = 9000/0.50 = 18000 kcal. Moles of methane = 18000/200 = 90 mol. Volume = 90 × 22.4 = 2016 l = 2.016 m 3 . This is option (b).

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