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3 years ago

11

In a movie theater in winter, 510 people, each generation sensible heat at a rate of 80 W, are watching a movie. The heat losses

through the walls, windows, and the roof are estimated to be 130,000 Btu/h. Determine the contribution of people to the heating of the building. The average rate of heat generation from people in a movie theater in sensible form is 80 W per person.

1 answer:

Harrizon [31]3 years ago

6 0

Answer:

$139213.68\ \text{Btu/h}$

Explanation:

Number of people = 510

Heat generated per person with respect to time = 80 W

$1\ \text{W}=3.4121\ \text{Btu/h}$

Heat generated by 510 people is

$\dot{Q}=510\times 80\times 3.4121$

$\Rightarrow \dot{Q}=139213.68\ \text{Btu/h}$

The contribution of people to the heating of the building is $139213.68\ \text{Btu/h}$

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Now that we know the value for k, we can find the moment the murder occur. A crucial information that the question left out is the temperature of a human body when they're still alive. A living human body is about 37ºC. We can use that as out initial temperature to solve this problem because we can assume that the freshly killed body will be around 37ºC.

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t = ??? we don't know how long it took from the time of the murder to when the police found the body

Rearrange the equation to solve for t

$T = T_m + (T_0-T_m)e^{kt}$

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plug in the values

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$t=\frac{ln(3/5)}{ln(8/9)}$

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The police found the body at 11:00PM so subtract 4.337 from that.

11 - 4.33 = 6.66 ≈ 6:30PM

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