Question

A sheet of aluminum weighing 100.0 g and at a temperature of 50.0 C is placed in contact with a piece of copper weighing 100.0 g and at a temperature of 100.0 C.

1) What do you expect to happen? Which metal is going to get warmer? Why? If you did not have a thermometer on the blocks, what visual cue would let you know one is hottter than the other?

2) Will the final temperature just be average of the two temperatures? If it was, what would the final temperature be? Show calculations please

3) Why do you think the effect heat capacity has on the final temperature of both metals.

4) Calculate how much heat or q the aluminum gained?

5) Calculate how much heat or q the copper lost?

6) List the change in temperature for each metal and explain the differences?

7) Finally, set up a calculation to determine the final temperature of the combined metals using the notion of the law of conservation of energy, pretending you do not know the final temperature from the experiment and see if you get the same final temperature.

Answer 1

(1) Heat will start flowing from hotter element ( Copper ) to the cooler one ( Aluminium ), because flow of heat always takes place from higher to lower temperature body. Thus, Aluminium will start getting warmer than 50'C.

At 100'C, since the water vaporizes, thus steam will start coming out of the surface of the hotter one because of vaporization of whatever water is present on its surface, even in very minute amounts.

(2)

If the final temp. was just the average of the two initial temperatures, then it will be : (100+50)/2 = 75'C

(3)

Because of different heat capacities, the final temperature will not be just the average. Assuming that Q amount of heat flows from copper to Al. Since Al has higher heat capacity(= 0.897 Jg^-1K^-1), its temperature will rise by less amount on absorbing Q heat, and temperature of Copper ( heat capacity = 0.385 Jg^-1K^-1) will fall by greater amount on releasing the same Q amount of heat.

(4)

Assuming final temp as 75'C,

heat gained by aluminium = m*Cp*dT = 100*0.897*(75-50) = 2242.5 J

(5)

Assuming final temp as 75'C,

heat lost by copper = m*Cp*dT = 100*0.385*(100-75) = 962.5 J

(6)

Change in temperature for both metals is the same (=25 'C). This is because we assumed in the beginning that final temp will be average of initial ones.

But this is not true, because both metals have different Cp values, due to which final temp will not be equal to 75'C.

Since we know that on transfer of Q amount of heat, Al will show small rise in temp, as compared to Cu which will show larger decrease in temp, the final temp will be between 50 and 75'C, as calculated below.

(7)

Assuming no heat loss to surroundings, and denoting final temp as T 'C :

Heat gained by Al = Heat lost by Cu

100*0.897*(T-50) = 100*0.385*(100-T)

Solving we get :

T = 8335/128.2 = 65.01 'C