Hi, how did you do question 14? I’m not aware of the equation (if there is one) that relates the variables in this question to pressure. Isn’t this Chemistry?
The equation is PV = nRT, where P is pressure, V is volume, T is temperature, n is the number of moles of the gas, and R is the gas constant. To answer the question you do need to know that the atomic weight of oxygen is 16 and carbon is 12, and hence be able to calculate the mass of carbon dioxide, and I guess this is kind-of chemistry, but I think that to be a good physicist you do need to know a bit about the elements …
The good news for our purposes, though, is that if you look at https://oxfordpat.wordpress.com/changes-to-the-syllabus/ you see that this is no longer on the syllabus. So no particular need to worry about it.
For question 13, the reason why length is divided by cube root of mass, is that volume is proportional to the cube of size, isn’t it?
Yes, volume is proportional to the cube of length. So since the density is unchanged, mass is proportional to the cube of length. Therefore the length of the locomotive is proportional to the cube root of its mass.
Could you explain me question 16, please?
First, imagine how you would assemble a big 5 x 5 x 5 cube from 125 identical little 1 x 1 x 1 cubes. There’s only one way of doing this: make a layer of 25 little cubes arranged in a 5 x 5 square, and then lay another 4 identical 5 x 5 square layers on top of this layer.
Second, suppose the little cubes were a bit sticky so that having assembled the big cube you could pick it up, and paint it. Which of the little cubes would get paint on it?
On the bottom square layer, all the cubes would have some paint on, because their bottoms are all painted, and on the top square layer, all the cubes would have some paint on because their tops are all painted.
In the three middle layers the tops and the bottoms of the cubes are unpainted, but any 1 x 1 cube on the outside of the square would be painted on one of its sides. However the little cubes not on the outside of the square would not have any paint on them. You should be able to see that there are nine cubes that are not on the outside of each square. So in each of these three layers, nine cubes are unpainted. Therefore a total of 27 cubes are unpainted.
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