Tea kettle question - part two

[JacksSmirkingRevenge]

Just so long as the milk isn't put in with the teabag first, it's all good.

[PsychoSerenity]

Psycho, admittedly I didn't check thorough through your calculations, but I think it is wrong to use the same k for both the tea and the mix in

T(t) = T2 + (T1 - T2) e^-kt

Clearly in normal circumstances a larger mass (tea+milk) will cool more slowly than a smaller one (only tea), so the k you are using is specific for a specific body (mass, form and material) and cannot be used as a constant in the way you do.

What people have been posting about here is only on factor in how k may be different. The probably most important factor in making up the difference in k lies in the different masses of the bodies.

Ahh I get you. And re-reading your second comment makes mores sense now - it was your first one that threw me. But surely adding the milk, I assume in a mug, elongates the cylinder, increasing the ratio of surface area to volume?

[Svartalf]

Just so long as the milk isn't put in with the teabag first, it's all good.

So, do you teabag the milkman too?

[MiM]

Psycho, admittedly I didn't check thorough through your calculations, but I think it is wrong to use the same k for both the tea and the mix in

T(t) = T2 + (T1 - T2) e^-kt

Clearly in normal circumstances a larger mass (tea+milk) will cool more slowly than a smaller one (only tea), so the k you are using is specific for a specific body (mass, form and material) and cannot be used as a constant in the way you do.

What people have been posting about here is only on factor in how k may be different. The probably most important factor in making up the difference in k lies in the different masses of the bodies.

Ahh I get you. And re-reading your second comment makes mores sense now - it was your first one that threw me. But surely adding the milk, I assume in a mug, elongates the cylinder, increasing the ratio of surface area to volume?

Yes, but in a normal teacup (porcelain) the transfer from the liquid to the wall and the lenghtwise transfer within the wall is efficient, and the limiting factor will be the transfer from the wall to the air (and table), which doesn't change much, as the size of the cup does not change, and the transfer from liquid to air, which doesn't change at all (giving a cylindrical cup).

With a cup made of a good insulator, the surface area will completely dominate, and this will not change at all.

[apophenia]

[Feck]

The tea (without milk) has a greater surface to volume ratio and it evaporates more quickly ..don't forget to factor that in .