Five metal samples, with equal masses, are heated to 200oc. each solid is dropped into a beaker containing 200 ml 15oc water. which metal will cool the fastest? a) aluminum b) copper eliminate c) gold d) platinum

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:

where:
is the heat exchanged
is the time interval
k is thermal conductivity of the material
A the  surface where the exchange of heat occurs
the variation of temperature
x is the thickness of the material
We see that the heat flow rate  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 :

where m is the mass and Cs the specific heat of the material. Re-arranging the formula, we get

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.

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If one were to put the y value into the equation, they could find out what x is for a certain value of y.  putting in the value of y (1), we get the equation: 1=4x-12=4xx=0.5this means that the value of x when why is 1 is x=0.5