1. Two aluminum rods A and B are such that rod A has twice the length of rod B w

Question

1. Two aluminum rods A and B are such that rod A has twice the length of rod B when they are at the same temperature. They are heated such that rod B experiences twice as great an increase in temperature as rod A.
Part 1) Which rod has the greater change in length? Explain briefly.

              a.) Rod A

              b.) Rod B

              c.) Both rods experience the same change in length

Part 2) Which rod has the greater fractional change in length? Explain briefly.

              a.) Rod A

              b.) Rod B

              c.) Both rods experience the same change in length?

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2. The temperature of an ideal gas is proportional to: (and briefly explain)

a.) the average velocity of the atoms

b.) the average momentum of the atoms

c.) the average kinetic energy of the atoms

d.) none of the above

Thanks!

Explanation / Answer

length of rod B is L length of rod A is L '= 2L change in length dL = L a dt for rod A , dt = dt So, dL = L ' a dt = 2L a dt for rod B ,dt ' = 2 dt So, dL ' = L a dt ' =L a 2dt = 2L a dt i.e., change in length of rod A and B are same. answer is Both rods experience the same change in length (b). fractional change in length of rod A is = change in length / original length = 2La dt / L ' = 2L a dt / 2L = a dt fractional change in length of rod B = 2L a dt / L = 2 a dt So, answer is rod B (2).The temperature of an ideal gas is proportional to the average kinetic energy of the atoms Since average kinetic enenrgy = kT / 2 from this temperature T is proportional to average kinetic energy

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