1-A copper collar is to fit tightly about a steel shaft whose diameter is 6.0017

Question

1-A copper collar is to fit tightly about a steel shaft whose diameter is 6.0017 cm at 22°C. The inside diameter of the copper collar at that temperature is 5.9800 cm. To what temperature must the copper collar be raised so that it will just slip on the steel shaft, assuming the temperature of both the steel shaft and copper collar are raised simultaneously?

? °C

2-

A container is filled to the brim with 1.5 L of mercury at 20°C. As the temperature of the container and mercury is increased to 56°C, a total of 7.8 mL of mercury spill over the brim of the container. Determine the linear expansion coefficient of the material that makes up the container.

? K-1

A room is 6.3 m by 5.2 m by 3 m.

1)

(a) If the air pressure in the room is 1 atm and the temperature is 298 K, find the number of moles of air in the room.
mol

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2)

(b) If the temperature rises by 5 K and the pressure remains constant, how many moles of air leave the room?

Explanation / Answer

Inner cross section is A1 = pi*r1^2 = 3.142*((5.98*10^-2)^2 = 0.011235 m^2

outer cross section is A2 = pi*r2^2 = 3.142*(6.0017*10^-2)^2 m= 0.011317 m^2

areal coefficient of copper is beta = 2*17*10^-6 = 34*10^-6 per deg C

we know that beta = (A2-A1)/(A1*dT)

change in temperature is dT = (A2-A1)/(A1*beta) = (0.011317-0.011235)/(0.011235*34*10^-6) = 214.66 deg C

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