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sdas [7]
4 years ago
5

If a refrigerator is a heat pump that follows the first law of thermodynamics, how much heat was removed from food inside of the

refrigerator if it released 492J of energy to the room? Joules
Mathematics
1 answer:
DaniilM [7]4 years ago
8 0
First, we need to define the first law of thermodynamics. This law states that in an isolated system, energy can neither be created nor destroyed, it can just be transformed from one form to another.

Based on this, if we assume that the refrigerator is and isolated system, then if 492 Joules of energy was released into the room, this means that 492 Joules of energy (heat) was removed from food inside the refrigerator. 
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f(x) = e^x sin (x)

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f'(x) = e^xsin(x)+e^x(cosx)= e^x(sinx+cosx)

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Now we pick a number between 0 to  \frac{3\pi }{4}

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f'(x) =e^{\frac{\pi }{2}}(sin(\frac{\pi}{2})+cos(\frac{\pi }{2}))

= 4.810 is positive

So the graph of f(x) is increasing on the interval [0, x=\frac{3\pi }{4})

Now we pick a number between   \frac{7\pi}{4} to 2pi

Lets pick  \frac{11\pi}{6}

Plug it into the derivative

f'(x) =e^{\frac{11\pi}{6}}(sin(\frac{11\pi}{6})+cos(\frac{11\pi }{6}))

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Increasing interval is (0,\frac{3\pi }{4}) U (\frac{7\pi }{4}, 2\pi)

Decreasing interval is (\frac{3\pi}{4}, \frac{7\pi}{4})

(b)

The graph of f(x) increases and reaches a local maximum at x=\frac{3\pi}{4}

The graph of f(x) decreases and reaches a local minimum at x=\frac{7\pi}{4}

(c)

f(0) = 0

f(2\pi)=0

f(\frac{3\pi }{4})=7.46

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Here global maximum at x=\frac{3\pi}{4}

Here global minimum at x=\frac{7\pi}{4}


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