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    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?

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    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: frac{Delta Q}{Delta t} = -k frac{A Delta T}{x} where:Delta Q is the heat exchangedDelta t is the time intervalk is thermal conductivity of the materialA the  surface where the exchange of heat occursDelta T the variation of temperaturex is the thickness of the materialWe see that the heat flow rate  frac{Delta Q}{Delta t} 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 temperatureTo solve this part, we can have a look at how the amount of heat exchanged Q is related to the increase in temperature Delta T:Q=m C_S Delta Twhere m is the mass and Cs the specific heat of the material. Re-arranging the formula, we getDelta T= frac{Q}{m C_s} 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. | Snapsolve

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    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

    Answer

    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:

    ΔQΔt = − k AΔTx where: Δ Q

    is the heat exchanged

    Δ t

    is the time interval

    k is thermal conductivity of the material

    A the  surface where the exchange of heat occurs

    Δ T

    the variation of temperature

    x is the thickness of the material

    We see that the heat flow rate

    ΔQΔt

    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

    Δ T : Q = m CS Δ T

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

    Δ T = QmCs

    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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