(adsbygoogle = window.adsbygoogle || []).push({}); PROBLEM 1 (work done by gas)

1. The problem statement, all variables and given/known data

1. An ideal monatomic gas originally in state A is taken reversibly to state B along the straight-line path shown in the pressure-volume graph. What ist he work done by the gas?

A) +12 cal

B) +122 cal

C) 0 cal

D) -110 cal

E) +110 cal

2. Relevant equations

4.186 calories per J

3. The attempt at a solution

I thought the area under the curve would be the work done by the gas, so I split it into a triangle and a rectangle and did this:

[tex]\frac{1}{2}(1)(101.3*10^{3})(2)(10^{-3}) = 101.3[/tex] (the area of the triangle)

[tex]2(101.3*10^{3})(2)(10^{-3}) = 405.2[/tex] (the area of the rectangle)

I added them up to get 506.5. I then divided by 4.186 to get 120.99, which I supposed was closest to 122.

The answer, however, is +110 cal.

PROBLEM 2 (RADIATION)

1. The problem statement, all variables and given/known data

2. Two identical solid spheres have the same temperature. One of the spheres is cut into two identical pieces. These two hemispheres are then separated. The intact sphere radiates an energy Q during a given time interval. During the same interval, the two hemispheres radiate a total energy of Q'. What is the ratio Q'/Q?

A) 1.5

B) 4.0

C) 0.50

D) 0.25

E) 2.9

2. Relevant equations

[tex]H = Aert^{4}[/tex]

3. The attempt at a solution

Not a clue how to start this one, as I don't have any values for r or t or A. My guess is those don't matter since H is directly proportional to A, so then I would have to find the surface area, however, I'm not sure how to compute the total surface area for Q' then.

The answer is 1.5, however.

PROBLEM 3 (coefficient of performance)

1. The problem statement, all variables and given/known data

3. If the coefficient of performance for a refrigerator is 5.0 and 65 J of work are done on the system, how much heat is rejected to the room?

A) 210 J

B) 260 J

C) 130 J

D) 330 J

E) 390 J

2. Relevant equations

[tex]COP = \frac{Q_{h}}{W}[/tex]

[tex]Q_{h} - Q_{c} = W[/tex]

3. The attempt at a solution

[tex]COP = \frac{Q_{h}}{W}[/tex]

[tex]COP = \frac{Q_{h}}{65} = 5[/tex]

[tex]Q_{h} = 325[/tex]

[tex]Q_{h} - Q_{c} = W[/tex]

[tex]325 - Q_{c} = 65[/tex]

[tex]Q_{c} = 260[/tex]

The answer, however, is 390, so I guess I am supposed to add 325 and 65, though I am not sure why.

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# 3 Thermodynamics problems [work done by gas, radiation, coefficient of performance]

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