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# PS_1 - these conditions What factors limit the maximum...

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Physics H7B Prof. I. Siddiqi Spring 2012 Problem Set #1 – Due in Class Tuesday 1/31/2012 #1. (a) The tube of a mercury thermometer has an inside diameter of 0.110 mm. The bulb has a volume of 0.190 cm 3. How far will the thread of mercury move when the temperature changes from 10.0°C to 20.0°C? Take into account expansion of the glass (Pyrex). (b) Determine a formula for the length of the mercury column in terms of relevant variables. [for mercury =180 x 10 -6 °C -1 ; for Pyrex, =3 x 10 -6 °C -1 ] #2. A hot-air balloon achieves its buoyant lift by heating the air inside the balloon which makes it less dense than the air outside. Suppose the volume of the balloon is 1800 m 3 and the required lift is 2700 N (rough estimate of the weight of the equipment and passenger). Calculate the temperature of the air inside the balloon which will produce the required lift. Assume the outside air temperature is 0°C and the air is an ideal gas under
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Unformatted text preview: these conditions. What factors limit the maximum altitude attainable by this method for a given load? (Neglect variables like wind). #3. From the known value of atmospheric pressure at the surface of the Earth, estimate the total number of air molecules in the Earth’s atmosphere. #4. A copper wire sags 50.0 cm between two utility poles 30.0m apart when the temperature is -15°C. Estimate the amount of sag when the temperature is +35°C. [Hint: An estimate can be made by assuming the shape of the wire is approximately an arc of a circle; hard equations can sometimes be solved by guessing values]. #5. Consider a container of oxygen gas at a temperature of 20°C that is 1.00 m tall. Compare the gravitational potential energy of a molecule at the top of the container (assuming the potential energy is zero at the bottom) with the average kinetic energy of the molecules. Is it reasonable to neglect the potential energy?...
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