TBR #2 Phys Questions

[aln012]

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51. Copper has a heat capacity of 0.118 cal/g·˚C. Aluminum has a heat capacity of 0.232 cal/g·˚C. What is the temperature of the mixture that results when equal parts of molten copper at 1300˚C and molten aluminum at 1310˚C are combined, assuming that no heat is lost to the surroundings?

A. 1300.0˚C B. 1303.3˚C C. 1305.0˚C D. 1306.7˚C D is the best answer. The heat capacity of aluminum at 1300˚C (0.232 cal/g·˚C) is roughly twice that of the heat capacity of copper at 1300˚C (0.118 cal/g·˚C). This means that when equal parts by mass of aluminum and copper are mixed, the final temperature should be closer to the initial temperature of aluminum than to the initial temperature of copper. The initial temperature of the aluminum component is 1310˚C, while the initial temperature of the copper component is 1300˚C. This means that the final temperature must be higher than 1305˚C, which makes choice D the best answer. The final temperature of the mixture can be found by setting the heat absorbed by the copper equal to the heat released by the aluminum. If we use the equation q = mC∆T, the following equality can be solved:

qabsorbed by Cu = - qreleased by Al
∴ massCu·CCu·(Tf - Ti) = - massAl·CAl·(Tf - Ti) = massAl·CAl·(Ti - Tf)
Given that massCu = massAl; CCu·(Tf - Ti) = CAl·(Ti - Tf)
∴ 0.118·(Tf - 1300) = 0.232·(1310 - Tf)
0.118 Tf - 1300(0.118) = 1310(0.232) - 0.232 Tf
∴ 0.350 Tf = 1310(0.232) + 1300(0.118)
0.350 Tf = 10(0.232) + 1300(0.232) + 1300(0.118) = 10(0.232) + 1300(0.350)

Adding 6.7 to 1300 gives 1306.7˚C. The best answer is D.




35. Which of the following reasons explains why a skidding car takes longer to stop than one that is not skidding?

A. A skidding tire transfers momentum more effectively than a rolling tire B. The coefficient of static friction between the car’s tires and the road surface is greater than the coefficient of kinetic friction B is the best answer. When a car does not skid, the kinetic friction between the brake pad and brake plate slows the wheels of the car; but it is actually the force of static friction between the tires and the road that eventually brings the vehicle to a stop. Alternatively, when a car skids, the force of kinetic friction between the tire and the road surface is what brings it to a stop. We know that a skidding car takes longer to stop than a car that is not in a skid. This is because the force of kinetic friction is less than the force of static friction needed to stop the vehicle. Static friction being greater than kinetic friction stems from the fact that the coefficient of static friction between the car's tires and the road surface is greater than the coefficient of kinetic friction. It should now be clear that choice B is true and choice D is the opposite of choice B and therefore false. If we think about choice C, it does not make much sense. A skidding car is losing mass (leaving part of the tire on the road), so it should also be losing momentum, and it should then also stop just a tiny bit faster, not more slowly. As for choice A, if a skidding tire transferred momentum better than a rolling tire, then it would lose momentum more readily and thus stop the car sooner than a rolling tire would. This opposes the basic premise of the question that a skidding tire takes longer to stop than a rolling tire. The best answer is B.


C. The skidding car loses some of the mass of its tires on the road surface D. The force of kinetic friction is greater than the force of static friction between the car’s tires and the road surface




Can someone help me conceptually view why a higher Heat Capacity substance added to a lower heat capacity substance would yield a final temperature towards that of the lower heat capacity substance?

And also the role of static friction vs. kinetic friction in stopping the car? I'm kind of confused by the explanations. Thanks a lot!

 

[MT Headed]

I will tackle the first one. Firstly, it will yield a final temperature closer to the substance with the higher heat capacity, if there are equal amounts of each material.

Conceptually, heat capacity is the amount of "oomph" (i.e. energy) it takes to get one gram of the substance to raise one degree. Metals typically have low heat capacities - it doesn't take much energy to heat a metal pot. Water has an enormous heat capacity - it takes a lot of energy to boil a pot of water. Be thankful for that. If you were made of metal instead of water, you would heat up a lot internally every time the sun came out, because you'd have a tiny little heat capacity.

As far as the question is concerned, some amount of energy is going to be exchanged between these two materials. Hotter aluminum is going to transfer some energy into colder copper until they are both the same temperature. That's the way the world works (2nd law of thermodynamics). But copper has a smaller heat capacity. So that same energy is going to affect copper more (raise its temperature more) than it will affect aluminum (lowering its temp just a little).

 

[aln012]

I get it! thanks a lot!