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OleMash [197]
2 years ago
7

imagine that 501 people are present in a movie theater of volume 8.00 x10^3 that is sealed shut so no air can escape. Each perso

n gives off heat at an average rate of 110 W. By how much will the temperature of the air have increased during a 2.0 h movie? The initial pressure is 1.01*10^5 Pa and the initial temperature is 20.0 degrees celcius
Physics
1 answer:
Semenov [28]2 years ago
8 0

Answer:

The temperature of air will increase by \Delta T=41044.967\ K

Explanation:

Given:

  • no. of person in a theater, n=501
  • volume of air in the theater, V=8\times 10^3\ m^3
  • rate of heat given off by each person, P=110\ J.s^{-1}
  • duration of movie, t=2\ hr=7200\ s
  • initial pressure in the theater, p_i=1.01\times 10^5\ Pa
  • initial temperature in the theater, T_i=20+273=293\ K
  • specific heat capacity of air at the given conditions, c=1.0061\ J.kg^{-1}.K^{-1}

<u>The total quantity of heat released by the total people in the theater during the movie:</u>

Q=n.P.t

Q=501\times 110\times 7200

Q=396792000\ J

<u>Form the relation of heat capacity:</u>

Q=m.c.\Delta T

∵p_i.V=m.R.T

Q=(\frac{p_i.V}{R.T}) \times c\times (T_f-T_i)

396792000=(\frac{1.01\times 10^5\times 8\times 10^3}{287\times 293}) \times 1.0061\times (T_f-293)

T_f=41337.967\ K

Change in temperature of air:

\Delta T=41044.967\ K

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