This is not a homework question! I'm having a discussion with a cost-conscious friend about the merits of reboiling the kettle full vs only boiling minimum amounts. We're both tea-lovers.
Assume:
- There is one person using the kettle to boil a cup of tea on the hour from 9am-4pm (8 cups).
- Assume a cup is a metric cup of water (250ml)
- The jug has a maximum capacity for 1.7L and a minimum capacity for 0.7L
- Electricity costs 33 cents per kilowatt-hour
- It takes 60 seconds to boil the jug when full from cold from cold start
- It takes 50 seconds to boil the jug at minimum from cold start
I'd like an equation to describe whether it is better to reboil or to only boil minimum amounts.
I don't know how to describe heat loss over time for this equation - I remember doing differential equations for melting snowballs in school - but I'm not sure how to apply it in this situation.
My question is: How to do an equation for whether to reboil the kettle full every hour or just minimum amounts?
You don't need a formal. It will take more energy to boil the full kettle than the partially full kettle. SO the first cup uses more energy if you have a full kettle. The full kettle will lose more energy in the 1 hour between cups because it remains hotter for longer so it gives off more heat. Think of the water that is not being used to make the tea. If it is on the tap at room temperature it is not losing any heat. If it is sitting in the kettle at a high temperature is is losing heat and therefore losing energy.