Question

If an amount of heat Q is needed to increase the temperature of a solid metal sphere of diameter D from 4°C to 7°C, the amount of heat needed to increase the temperature of a solid sphere of diameter 2D of the same metal from 4°C to 7°C is

Answer 1

Q = c M ΔT where c is the heat capacity and M the mass present

Q2 / Q1 = M2 / M1 since the other factors are the same

M = ρ V where ρ is the density

M = ρ Π (d / 2)^2 where d is the diameter of the sphere

M2 / M1 = (2 D/2)^2 / (D/2)^2 = 4

It will take 4Q heat to heat the second sphere