KWh confusion

From the unit 4 Jan 2011 paper:

A domestic refrigerator works at a mean power of 70 W. Calculate the cost of running this refrigerator for one week at a cost of 12 p per kWh.

The mark scheme has the working out as (70/1000) * 7 * 24 = 11.8kWh

I don't understand why it isn't (70/1000) * 60 * 60 * 7 * 24. Surely 70W is 70J/s not 70J/hour unless it's something to do with the 'mean power'?

Any help is appreciated.

Reply 1

Joinedup

20

Original post by COMC

From the unit 4 Jan 2011 paper:

A domestic refrigerator works at a mean power of 70 W. Calculate the cost of running this refrigerator for one week at a cost of 12 p per kWh.

The mark scheme has the working out as (70/1000) * 7 * 24 = 11.8kWh

I don't understand why it isn't (70/1000) * 60 * 60 * 7 * 24. Surely 70W is 70J/s not 70J/hour unless it's something to do with the 'mean power'?

Any help is appreciated.

In the markscheme the calculation for number of Joules per week has been combined with the conversion from Joules to kWh... the multiply by (60*60) has been cancelled by dividing by (60*60)

you don't need to reproduce markscheme answers, they're not model answers or the style of answer that the exam board prefers to see - if you're happier calculating the number of Joules per week and then doing a separate calculation to convert units from Joules to kWh then do it that way.

Reply 2

Kallisto

Entertainment Forum Helper

22

Original post by COMC

From the unit 4 Jan 2011 paper:

A domestic refrigerator works at a mean power of 70 W. Calculate the cost of running this refrigerator for one week at a cost of 12 p per kWh.

The mark scheme has the working out as (70/1000) * 7 * 24 = 11.8kWh

I don't understand why it isn't (70/1000) * 60 * 60 * 7 * 24. Surely 70W is 70J/s not 70J/hour unless it's something to do with the 'mean power'?

Any help is appreciated.

As Joinedup said, it is cancelled by conversion from Joule to kWh.

As 70W is 70J/s (so per second!), it is 60*60 to convert from second to hour. Multiply this product by 1000 to come from W to kW is also right.

So it is (70/1000*60*60). To get the costs for one week in hours, you calculate 60*60*24*7. When you calculate the kWh for one week in hours, the product 60*60 will cancel out, as it is both in numerator and denominator:

(70/1000*60*60) * 60*60*24*7 = (70/1000)*7*24

That leads to the calculation your markscheme has worked out.

Original post by Kallisto

So it is (70/1000*60*60). To get the costs for one week in hours, you calculate 60*60*24*7. When you calculate the kWh for one week in hours, the product 60*60 will cancel out, as it is both in numerator and denominator:

(70/1000*60*60) * 60*60*24*7 = (70/1000)*7*24
.....

Sorry I don't see how the last expression is equivalent. :smile:

Reply 4

COMC

OP

2

Thanks guys. That cleared it up for me.

Reply 5

Kallisto

Entertainment Forum Helper

22

Original post by Eimmanuel

Sorry I don't see how the last expression is equivalent. :smile:

I am sure that I have cancelled out the product 60*60 on the right side of the equation? :hmmmm2:

Original post by COMC

Thanks guys. That cleared it up for me.

That is nice to hear! :h:

Original post by Kallisto

I am sure that I have cancelled out the product 60*60 on the right side of the equation? :hmmmm2:

I tend to hear "I am sure...." but ...

I would let wolfram alpha do the "unbiased" evaluation.

(70/1000*60*60) * 60*60*24*7
http://www.wolframalpha.com/input/?i=(70%2F1000*60*60)+*+60*60*24*7

(70/1000)*7*24
http://www.wolframalpha.com/input/?i=(70%2F1000)*7*24

Still LHS = RHS? :hmmmm2:

Reply 7

Kallisto

Entertainment Forum Helper

22

Original post by Eimmanuel

x

You are very precisely with written fractions, but you are right!

(70/(1000*60*60)) * 60*60*24*7 = (70/1000)*7*24

Is this with double brackets on left side better now?