Pc1431 Assignment 8-1





Part DWhat is the final volume ?Hint D.1

Relation between volume and temperature

Recall that, in an adiabatic process with finite changes in volume and temperature, is aconstant. As a result, . ANSWER:=



Work from an Adiabatic Expansion

In this problem you are to consider an


 expansion of an ideal diatomic gas, which means thatthe gas expands with no addition or subtraction of heat.This appletshows the adiabatic compression and expansion of an ideal monatomic gas with . Itwill help you to see the qualitative behavior of adiabatic expansions, though your actual calculations willuse a slightly different . Assume that the gas is initially at pressure , volume , and temperature . In addition, assume thatthe temperature of the gas is such that you can neglect vibrational degrees of freedom. Thus, the ratio of heat capacities is .Note that, unless explicitly stated, the variable should not appear in your answers--if needed use thefact that for an ideal diatomic gas.Part AFind an analytic expression for , the pressure as a function of volume, during the adiabaticexpansion.Hint A.1

Find the conserved quantity in an adiabatic process

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Express the pressure in terms of and any or all of the given initial values , , and .



The fact that is a constant derives from the definition of an adiabatic process as one inwhich no heat flow into or out of the system occurs. Setting in the first law of 


Assignment 1: Kinematics in 2 and 3 Dimensions

Due: 2:00am on Saturday, September 4, 2010


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Arrow Hits Apple

 An arrow is shot at an angle of above the horizontal. The arrow hits a tree a horizontal distance away, at the same height above the ground as it was shot. Use for themagnitude of the acceleration due to gravity.Part AFind , the time that the arrow spends in the air.Hint A.1

Find the initial upward component of velocity in terms of D.

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Hint A.2

Find the time of flight in terms of the initial vertical component of velocity.

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Hint A.3

Put the algebra together to find symbolically.

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Answer numerically in seconds, to two significant figures.




Suppose someone drops an apple from a vertical distance of 6.0 meters, directly above the pointwhere the arrow hits the tree.Part BHow long after the arrow was shot should the apple be dropped, in order for the arrow to pierce theapple as the arrow hits the tree?Hint B.1

When should the apple be dropped

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Hint B.2

Find the time it takes for the apple to fall 6.0 meters

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Express your answer numerically in seconds, to two significant figures.




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