...time of a joint of meat? I'm really struggling with a question set by my tutor at Uni. It's quite specific I think. On a sheet titled "Partial Derivatives", he says:

"The cooking time, t, of a joint of meat depends on its mass, m, density, ρ, specific heat capacity, C, and thermal conductivity, κ. Use dimensional analysis to deduce how the cooking time depends on the mass of the joint..."

Now, I know (or at least, I'm pretty sure) the units for these are:

C = [J kgˉ¹ Kˉ¹] = [m² sˉ¹ Kˉ¹];
κ = [W mˉ¹ Kˉ¹] = [kg m sˉ¹ Kˉ¹];
m = [kg];
t = [s];
ρ = [kg mˉ³].

So, it is obvious that to eliminate the Kelvins, the heat capacity and thermal conductivity must equate, but this leaves no seconds with which to balance the time - so I added temperature, T [K].

Now I don't have to balance the Kelvins, but I *do* have to balance the metres using C, κ and ρ. I've managed this by

(Cκ)/ρ,

however, this leaves no kilogrammes to balance the mass with!

Please, please help, it's driving me mad! Thanks.