An aluminum rod 0.500 m in length and with a cross sectional area of 2.50 cm2 is inserted into a thermally insulated vessel containing liquid helium at 4.20 K. The rod is initially at 3(H) K. (a) If one-halt of the rod is inserted into the helium, how many liters of helium boil off by the time the inserted half cools to 4.20 K? Assume the upper half does not yet cool, (b) If the circular surface of the upper end of the rod is maintained at 300 K. what is the approximate boil-off rate of liquid helium in liters per second after the lower half has reached 4.20 K? (Aluminum has thermal
(a)
The volume of helium boil off by the time the inserted half cools is
Answer to Problem 20.61AP
The volume of helium boil off by the time the inserted half cools to
Explanation of Solution
Given info: The length of the aluminum rod is
Write the expression for the mass of the substance.
Here,
The expression for the volume of the rod is,
Here,
Substitute
For the mass of the aluminum rod:
Substitute
Thus, the mass of the aluminum rod is
For the mass of the helium:
Substitute
Here,
Write the expression for the amount of heat lost by the aluminum rod due to the change in temperature.
Here,
Substitute
Thus, the heat lost by the aluminum rod is
Write the expression for the heat gained by the helium.
Here,
Substitute
From the law of the conservation of energy, the heat lost is equal to the heat gained.
Write the expression for the heat lost by the aluminum rod is equal to the heat gained by the helium.
Substitute
Thus, the volume of helium boil off by the time the inserted half cools to
Conclusion:
Therefore, the volume of helium boil off by the time the inserted half cools to
(b)
The boil off rate of liquid helium when the lower half reached
Answer to Problem 20.61AP
The boil off rate of liquid helium when the lower half reached
Explanation of Solution
Given info: The length of the aluminum rod is
Write the expression for the rate at which energy is supplied to the rod.
Here,
Substitute
Thus, the rate at which energy is supplied to the rod is
Write the expression for the boil off rate of liquid helium after the lower half reaches
Substitute
Conclusion:
Therefore, the boil off rate of liquid helium when the lower half reached
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Chapter 20 Solutions
Physics for Scientists and Engineers (AP Edition)
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