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 α_iron 1.2 X 10^-5/ K and α_brass 1.8 X 10^-5 /K , what should we take as length of each strip?

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?

[S_w = 1 cal/g/° C and L^w _fusion = 80 cal/ g]

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.

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 (β_vbrass = 6 × 10^-5/K and β_viron = 3.55 ×10_-5 / K) to create a volume of 100 cc. How do you think you can achieve this?

Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of 57^o C is drunk. You can take body (tooth) temperature to be 37o C and α = 1.7× 10^-5 /^o C, bulk modulus for copper = 140 × 10 ⁹ N/m2.