Explanation Given data: The basketball attendance record is 33 , 633 , the volume of air in the dome is about 1.5 × 10 6 m 3 , and the rate of the metabolic thermal energy transferred by each person to the air in the dome is 100 W ( 100 J/s ) . Formula used: The thermal energy transferred to the air by the entire audience via metabolism is given by the expression as follows: Q = N P Δ t Here, N is the number of the persons in the audience, P is the rate of metabolic thermal energy, and Δ t is the time. The mass of air is given by the expression as follows: m = ρ V Here, ρ is the density of air and V is the volume of the air. Write the expression for thermal energy in terms of temperature change. Q = m c Δ T Here, c is the specific heat of air, m is the mass of the air, and Δ T is the required temperature change. Explanation: Suppose that the volume of the air inside the dome stays constant, so no work is done on the air by the environment. The change in the thermal energy of the gas is considered equivalent to the energy transferred by the spectators. The thermal energy transported to the air by the whole audience via metabolism can be calculated as follows: Q = N P Δ t Substitute 33633 for N , 100 J/s for P , and 2 h for Δ t . Q = ( 33633 ) ( 100 J/s ) [ 2 h ( 60 × 60 s 1 h ) ] = 2.42 × 10 10 J Recall the expression for the mass of air in the dome. m = ρ V Assume the density of air to be 1

2nd Edition

ISBN: 9780134601823

Author: ETKINA, Eugenia, Planinšič, G. (gorazd), Van Heuvelen, Alan

Publisher: Pearson,

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Chapter 15, Problem 15P

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The change in temperature of the air within 2 h when the seats in the dome are occupied and the metabolic thermal energy transferred, by each person, to the air is at a rate of 100 W(100 J/s); the dome has a volume of 1.5×106 m3, assuming there is no loss in thermal energy.

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The change in temperature of the air within 2 h when the seats in the dome are occupied and the metabolic thermal energy transferred, by each person, to the air is at a rate of 100 W ( 100 J/s ) ; the dome has a volume of 1.5 × 10 6 m 3 , assuming there is no loss in thermal energy.

Solution Summary: The author explains how the change in the temperature of the air is considered equivalent to the energy transferred by the spectators.

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The change in temperature of the air within 2 h when the seats in the dome are occupied and the metabolic thermal energy transferred, by each person, to the air is at a rate of 100 W(100 J/s); the dome has a volume of 1.5×106 m3, assuming there is no loss in thermal energy.

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Chapter 15 Solutions