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3 years ago

15

A room is cooled by circulating chilled water through a heat exchanger located in the room. The air is circulated through the he

at exchanger by a 0.25-hp (shaft output) fan. Typical efficiency of small electric motors driving 0.25-hp equipment is 60 percent. Determine the rate of heat supply by the fan–motor assembly to the room.

1 answer:

Zanzabum3 years ago

6 0

Answer:

input power of the geothermal motor will be 0.4166 hP

Explanation:

We have given shaft output = 0.25 hP

hP is known as horse power which is unit of measuring the power of motor

Efficiency of motor is given as efficiency = 60 % = 0.6

We have to fond the heat supply by the fan motor Q

We know that efficiency of any motor is the ratio of shaft power and input power

So $0.6=\frac{0.25}{P_0}$

So $P_0=\frac{0.25}{0.6}=0.4166hP$

So input power of the geothermal motor will be 0.4166 hP

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Explanation:

Newton's law of cooling states:

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

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$T_0$ = initial temp

$T_m$ = temp of room

$T$ = temp after t hours

$k$ = how fast the temp is changing

$t$ = time (hours)

$T_0 = 31$ because the body was initlally 31ºC when the police found it

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$T = 30$ because the body temp drop to 30ºC after 1 hour

t = 1 because that's the time it took for the body temp to drop to 30ºC

$k=???$ we don't know k so we must solve for this

rearrange the equation to solve for k

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

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

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

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$\frac{ln(\frac{T - T_m}{T_0-T_m})}{t}=k$

plug in the numbers to solve for k

$k = \frac{ln(\frac{T - T_m}{T_0-T_m})}{t}$

$k = \frac{ln(\frac{30 - 22}{31-22})}{1}$

$k=ln(\frac{8}{9})$

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.

$T_0 = 37$ because the body was 37ºC right after being killed

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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

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plug in the values

$t=\frac{ln(\frac{T - T_m}{T_0-T_m})}{k}$

$t=\frac{ln(\frac{31 - 22}{37-22})}{ln(8/9)}$

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

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

t ≈ 4.337 hours from the time the body was killed to when the police found it.

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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