Help with thermodynamics basics? Due at midnight, please help! Questions 5 -7 re

Question

Help with thermodynamics basics? Due at midnight, please help!

Questions 5 -7 refer to two identical cups, A and B, each containing 100 grams of water. The cups are in a room where the temperature is 25 degreeC. The water in cup A is initially at 55 degreeC, while that in cup B is initially at 40 degreeC. Initially, which cup will cool down at a faster rate? Which cup will reach its final temperature most quickly? Which of the following graphs best represents the shape of the graph of the temperature of cup A over time? Answer H if you think that none is correct. (Note that the origin does not necessarily represent 0 degree C) Cup A contains 100 grams of water at 0 degreeC and cup B contains 100 grams of water at 50 degreeC. The contents of the two cups are mixed together in an insulated container (no heat can transfer in or out). The final temperature of the water in the container is Cup A again contains 100 grams of water at 0 degreeC but cup B now contains 200 grams of water at 50 degreeC. The contents of the two cups are mixed together in an insulated container (no heat can transfer in or out). The final temperature of the water in the container is

Explanation / Answer

(5) We know that the the heat transfer rate is directly proportional to the temperature difference.
therefore the Cup A will cool faster initially.
(6) Since the heat tranfer depends upon the temperature difference but here continuously temperature will change tehrefore Cup B will get to its temperature quickly.

(7) D represent the graph.
(8) Since mass is same therefore the final temperature will be average of the inital
i.e 25 C
(9) In this case assume final temperaure is T
100C(T-0) =200C(50 -T)
T = 100 -2T
T = 100/3 = 33.33 C
Hence E is the option

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