Chapter 11: Thermal Properties of Matter

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 to bring mixture to a comfortable temperature. Suddenly Ramesh had to attend something which would take some times, say 5-10 minutes before he could take bath. Now he has two options:

a) fill the remaining bucket completely by cold water and then attend the work

b) 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 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 would change in such a way that difference between their lengths remain constant. If α_iron = 1.2 × 10^-5/K and α_brass = 1.8 × 10^-5/K, what should we take as length of each strip?

We would like to make a vessel whose volume does not change with temperature. We can use brass and iron (β_brass = 6 × 10^-6/K and β_iron = 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^oC is drunk. You can take body temperature to be 37^oC and α = 1.7 × 10^-5oC, bulk modulus for copper = 140 × 10⁹ N/m².

A rail track made of steel having length 10 m is clamped on a railway line at its two ends. On a summer day due to rise in temperature by 20^oC, it is deformed as shown in the figure. Find x if α_steel = 1.2 × 10^-5/^oC.

A thin rod having length Lo at 0^oC and coefficient of linear expansion α has its two ends maintained at temperatures θ₁ and θ₂, respectively. Find its new length.

According to Stefan’s law of radiation, a black body radiates energy σT⁴ from its unit surface area every second where T is the surface temperature of the black body and σ = 5.67 × 10^-8 W/m²K⁴ is known as Stefan’s constant. A nuclear weapon may be thought of as a ball of radius 0.5 m. When denoted, it reaches temperature of 106K and can be treated as a black body.

a) estimate the power it radiates

b) if surrounding has water at 30^oC, how much water can 10% of the energy produced evaporate in 1 sec?

c) if all this energy U is in the form of radiation, corresponding momentum is p = U/c. How much momentum per unit time does it impart on unit area at a distance of 1 km?