# Oxford PAT 2013, Question 20

N.B. there is a silly mistake in the answer to the final section below, kindly pointed out by Mwana in the comments section.

## 2 thoughts on “Oxford PAT 2013, Question 20”

1. Mwana says:

Would it be incorrect to compare using t he energies. I did, 504kj was gained in 15minutes at sea level so if the power was to reduce to 50% then the time taken would double so 504kj would take 30 minutes instead. Hence you compare and find out how long 29.4kj (the energy to boil 100g of water when she is 6000m above) would take. This give me 1.8 minutes or 108 seconds.

1. Thanks for your comment Mwana.

I’m not sure where you get your final value from. But there is a stupid arithmetical error in my calculation above. Here’s what it should say:

The first line is correct. The power at sea level = P = (4.2 x 120) / (15 x 60)

But in the second line I have halved the time instead of doubling it! It should read:

Time to boil cup = (4.2 x 0.1 x 70) / (P / 2) = (2 x 4.2 x 0.1 x 70) / P

So this equals (2 x 4.2 x 0.1 x 70 x 15 x 60) / (4.2 x 120) = 7 x 15 = 105 seconds.

So you are a lot closer than I was, but I think you should check your arithmetic too. Your reasoning is correct: the power at altitude is 504 / (30 x 60) = 0.28kW. The energy to boil the cup at altitude is 29.4kW. Therefore the time is 29.4/0.28, which I make equal to 105 seconds.

The motto is pretty obvious: never ask a physicist to use actual numbers, it’s asking for trouble!