How do you calculate temperature?

For task 3:

First determine the temperature difference between 18° C. and -35° C. This is called ΔT (“Delta T”). ΔT has a negative amount in this case because the temperature decreases.

Now you need to paint ΔT with the volume expansion coefficient γ (“Gamma”) of brass. This results in the relative volume change ΔV/V around which the brass is contracted when it is cooled by ΔT. Attention, the unit of γ is incorrectly specified in the task: it is not cm3/°C, but 1/°C. If you calculate ΔT times γ, then °C is abbreviated and the result, i.e. ΔV/V, is a number without unit, in this case a negative number.

Now you can consider what the new volume V2 of the brass is. Before it was V, and now it is V+ΔV. With the relative volume change ΔV/V, you can then say: V2 =V*(1+ΔV/V). It follows that the volume has changed by the factor V2/V=1+ΔV/V.

Now we come to the solution, the changed density. The density = mass/volume. The mass has remained the same. The new density ρ2 is therefore mass/new volume.

ρ = m/V

ρ2 = m/V2

The ratio of the new to the old density is thus:

ρ2/ρ = V/V2

ρ2/ρ = 1/(1+ΔV/V)

ρ2 = ρ/(1+ΔV/V)

Since we have cooled the brass and ΔV is negative, 1+ΔV/V < 1, i.e. the density has increased, i.e. ρ2 is greater than ρ.