Units in a heat transferred calculation

[smulc]

I'm trying to do a calculation using: Heat transferred = mass x specific heat capacity x change in temperature
q=mc∆T

But the value I'm trying to calculate is the change in temperature so I've rearranged the equation to ∆T= q/mc

I think the numbers and answer I have are correct, but the units are confusing me. My answer clearly needs to be in °C, the joules on the top and the bottom will cancel out but then on the bottom I'm left with kg multiplied by kg^-1.

3.54 J
450 kg x 4.2 x 10³ J kg^-1 °C^-1

As far as I know, these don't cancel each other out so my answer has the wrong units. I don't know if I've done the entire thing wrong if I'm just confusing myself over something silly. I'd appreciate any help at all.

 

[Redbelly98]

... on the bottom I'm left with kg multiplied by kg^-1.

So are you wondering what to do with kg·kg^-1?

kg is the same as kg⁺¹, so what you really have is kg⁺¹·kg^-1. Simplify that using algebra rules for exponents, and you should be all set.

 

[smulc]

ohh I feel really stupid now. Any number to the zero power is equal to 1. I already knew this but mistakingly thought that the result of calculating kg⁰ would be 1kg, but the answer is literally just 1, isn't it? So the kg does actually cancel. I feel silly for not realising, thanks very much for the help!

 

[Redbelly98]

You're welcome, glad it worked out for you.