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Ede4ka [16]
3 years ago
15

A teacher wants to demonstrate that unheated water can boil at room temperature in a beaker within a bell jar connected to a vac

-uum pump. However, the vacuum pump is faulty and can reduce pressures only to 15 kPa. Can the teacher use this pump to perform the demonstra-tion successfully? Explain your answer.
Physics
1 answer:
laiz [17]3 years ago
8 0

Answer:

No .

Explanation:

The vapor pressure of water at room temperature is .0313 atom  or 3.13 kPa.

To make a liquid boil, its vapor pressure must be  equal to pressure around it.

So pump must create pressure of 3.13 k Pa or less to make water attain its stage of boiling at room temperature. As the motor  can not produce pressure lesser than 15 k Pa , pump will not be able to make water boil at room temperature.

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Let us say that x is the cut that we will make on the sides to make a box, therefore the new dimensions are:

l = 15 – 2x

w = 8 – 2x

It is 2x since we cut on two sides.

 

We know that volume is:

V = l w x

V = (15 – 2x) (8 – 2x) x

V = 120x – 30x^2 – 16x^2 + 4x^3

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Taking the 1st derivative:

dV/dx = 120 – 92x + 12x^2

 

Set dV/dx = 0 to get maxima:

120 – 92x + 12x^2 = 0

 

Divide by 12:

x^2 – (92/12)x + 10 = 0

(x – (92/24))^2 = -10 + (92/24)^2

x - 92/24 = ±2.17

x = 1.66, 6

We cannot have x = 6 because that will make our w negative, so:

x = 1.66 inches

 

So the largest volume is:

V = 120x – 46x^2 + 4x^3

V = 120(1.66) – 46(1.66)^2 + 4(1.66)^3

V = 90.74 cubic inches

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Answer:

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