Part 1) Which metal will cool the fastest?
To answer this question, we should have a look at the formula of the heat flow rate, which says "how fast" a material is able to heat/cool:
[tex] \frac{\Delta Q}{\Delta t} = -k \frac{A \Delta T}{x} [/tex]
where:
[tex]\Delta Q[/tex] is the heat exchanged
[tex]\Delta t[/tex] is the time interval
k is thermal conductivity of the material
A the surface where the exchange of heat occurs
[tex]\Delta T[/tex] the variation of temperature
x is the thickness of the material
We see that the heat flow rate [tex] \frac{\Delta Q}{\Delta t} [/tex] is linearly proportional to k, the thermal conductivity of the material. So, the larger k, the fastest the metal will cool.
If we have a look at the thermal conductivity of each metal, we find:
- Aluminium: 237 W/(mK)
- Copper: 401 W/(mK)
- Gold: 314 W/(mK)
- Platinum: 69 W/(mK)
Therefore, copper is the material with highest heat flow rate, so the metal which cools fastest.
Part 2) Which sample of copper demonstrates the greatest increase in temperature
To solve this part, we can have a look at how the amount of heat exchanged Q is related to the increase in temperature [tex]\Delta T[/tex]:
[tex]Q=m C_S \Delta T[/tex]
where m is the mass and Cs the specific heat of the material. Re-arranging the formula, we get
[tex]\Delta T= \frac{Q}{m C_s} [/tex]
therefore, we see that the increase in temperature is inversely proportional to the mass m. This means that the block that will show the largest increase in temperature is the block with the smallest mass, so the correct answer is A) 0.5 kg.
