A gas water heater burns natural gas (methane, CH4). Each gram of natural gas bu

Question

A gas water heater burns natural gas (methane, CH4). Each gram of natural gas burned yields approximately 13,000 calories of energy. A typical water heater takes in water at about 20oC (68oF) and raises its temperature to 60oC (140oF). A typical “low-flow” shower-head might use around 10L of water per minute (which we can estimate 5L of hot water and 5L of cold water mixed), and a typical shower might last 8 minutes. A liter of water has a mass of 1000g. So, how much natural gas does a typical shower require?.

Explanation / Answer

A typical shower takes 5 L of Hot water per minute.
A typical shower last 8 minutes.

So A typical shower takes 8 x 5 = 40 litres of hot water.

Given: 1 litre of water has mass of 1000 grams

So a typical shower takes 40 x 1000 = 40000 grams of hot water.

Heat Energy required to turn 40000 grams of water hot
= mass x SpecificHeat x temperatureDifference

mass = 40000 grams
specific heat of water = 1 calorie/(gram oC)
temperature difference = 60 - 20 = 40 oC

So Heat Required = 40000 x 1 x 40 = 16 x 105 Calories

Now 1 gram of methane produces 13000

So ammount of methane required for a typical shower = (16 x 105 )/ 13000 grams

= 123 grams

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