Q25 of 27 Page 82

A rail track made of steel having length 10 m is clamped on a railway line at its two ends (Fig 11.3). On a summer day due to rise in temperature by 20° C, it is deformed as shown in figure. Find x (displacement of the center) if αsteel = 1.2× 10-5 /°C.

image1.png


Here, we apply Pythagoras theorem to find x in terms of L.

From the figure, it is clear that




As, ΔL2 is a very small quantity, we can neglect it.



(here, we multiply and divide 2 in the numerator and denominator)


We know,




Here,


αsteel = 1.2× 10-5 /°C and ΔT = 20 °C. Therefore,



So, the displacement is about 11 cm.


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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?

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Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of 57o 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.

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A thin rod having length L0 at 0° C and coefficient of linear expansion α has its two ends maintained at temperatures θ1 and θ2, respectively. Find its new length.

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According to Stefan’s law of radiation, a black body radiates energy σT 4 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 detonated, 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 C°, how much water can 10% of the energy produced evaporate in 1 s?


[Sw = 4186.0 J/ kgK and Lv = 22.6 X 105 J / kg]


(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?