Q: Coefficient of linear expansion (K-1 ): Brass (2E-5), Copper (1.7E-5), Steel

Question

Q:

Coefficient of linear expansion (K-1 ): Brass (2E-5), Copper (1.7E-5), Steel (1.2E-5)

Coefficient of Volume expansion (K-1 ): Brass (6E-5), Copper (5.1E-5), Steel (3.6E-5)

Problems:

1) Text (17.21) A machinist bores a hole of diameter 1.35 cm. in a steel plate at a temperature of 25.0 o C. What is the cross sectional area of the hole (a) at 25 o C, and (b) when the temperature of the plate is increased by 175 o C? Assume the coefficient of linear expansion remains constant over this temperature range.

2) Text (17.38) As a physicist, you put heat into a 500.0 g. solid sample at the rate of 10.0 kJ/min, while recording its temperature as a function of time. You plot your data and obtain the graph shown below. (a) What is the latent heat of fusion for this solid? (b) What are the specific heats of the liquid and solid states of the material?

3) Text (17.82) You pour 108 cm3 of ethanol, at a temperature of -10 o C, into a graduated cylinder initially at 20 o C, filling it to the very top. The cylinder is made of glass with a specific heat 0.84 kJ/kg.K and a coefficient of volume expansion of 1.2 X 10-5 / K. its mass is 0.110 kg. The mass of the ethanol is 0.0873 kg. (a) What will be the final temperature of the ethanol, once thermal equilibrium is reached? (b) How much ethanol will overflow the cylinder before thermal equilibrium is reached? (From Table 17.2 and 17.3, ethanol volume expansion coefficient 75 X 10-5 / K, ethanol specific heat 2428 J/kg.K ).

4) As shown in figure below, suppose that the rod in the figure is made of Cu, if 45.0 cm long and has a cross-section area of 1.25 cm2 . Let TH = 100 o C and TC = 0.0 o C. (a) What is the final steady-state temperature gradient along the rod? (b) What is the heat current in the rod in the final steady state? (c) What is the final steady-state temperature at a point in the rod 12.0 cm from its left end?

5) Text (17.101) A copper calorimeter can with mass 0.446 kg contains 0.0950 kg of ice. The system is initially at 0.0 o C (a) if 0.0350 kg of steam at 100.0 o C and 1.00 atm pressure is added to the can, what is the final temperature of the calorimeter can and its contents? (b) At the final temperature, how many kilograms are there of ice, how many of liquid water, and how many of steam? (From Table 17.3 and 17.4, water latent heat of vaporization 2.256 X 106 J/kg, water latent heat of fusion 3.34 X 105 J/kg, water specific heat 4.19 kJ/kg-K, copper specific heat 390 J/kg-K).

Explanation / Answer

Here ,

initial diameter of hole , d = 1.35 cm

at T = 25 degree C

a)

area of cross section of hole = pi * (1.35/2)^2

area of cross section of hole = 1.43 cm^2

area of cross section of hole at 25 degree C is 1.43 cm^2

b) at T = 175 degree C

diamter of hole , d = 1.35 *(1 + 1.2 *10^-5 * (175 - 25))

d = 1.35243 cm

area of cross section = pi * (1.35243)^2/4

area of cross section = 1.4363 cm^2

the area of cross section at 175 degree C is 1.4363 cm^2

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