Q21 of 27 Page 81

One day in the morning, Ramesh filled up 1/3 bucket of hot water from geyser, to take bath. Remaining 2/3 was to be filled by cold water (at room temperature) to bring mixture to a comfortable temperature. Suddenly Ramesh had to attend to something which would take some times, say 5-10 minutes before he could take bath. Now he had two options: (i) fill the remaining bucket completely by cold water and then attend to the work, (ii) first attend to the work and fill the remaining bucket just before taking bath. Which option do you think would have kept water warmer? Explain.

The rate of heat energy loss is directly proportional to the difference in temperature. In the first scenario, mixing the cold water with the hot water overall brings the water to an intermediate temperature which isn’t too hot. The difference between this intermediate temperature and the surrounding temperature is less. Hence the heat loss would be less. In the second scenario, the temperature difference between the hot water and the surrounding is considerable and thus, the heat loss will occur rapidly. This will cool the water down.

So, the first option will keep the water warmer.


More from this chapter

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19

During summers in India, one of the common practices to keep cool is to make ice balls of crushed ice, dip it in flavored sugar syrup and sip it. For this a stick is inserted into crushed ice and is squeezed in the palm to make it into the ball. Equivalently in winter, in those areas where it snows, people make snow balls and throw around. Explain the formation of ball out of crushed ice or snow in the light of P–T diagram of water.

 20

100 g of water is supercooled to –10° C. At this point, due to some disturbance mechanized or otherwise some of it suddenly freezes to ice. What will be the temperature of the resultant mixture and how much mass would freeze?

[Sw = 1 cal/g/° C and Lw fusion = 80 cal/ g]


 22

We would like to prepare a scale whose length does not change with temperature. It is proposed to prepare a unit scale of this type whose length remains, say 10 cm. We can use a bimetallic strip made of brass and iron each of different length whose length (both components) would change in such a way that difference between their lengths remain constant. If αiron 1.2 X 10-5/ K and αbrass 1.8 X 10-5 /K , what should we take as length of each strip?

 23

We would like to make a vessel whose volume does not change with temperature (take a hint from the problem above). We can use brass and iron (βvbrass = 6 × 10-5/K and βviron = 3.55 ×10-5 / K) to create a volume of 100 cc. How do you think you can achieve this?