What is the coefficient of performance of this refrigerator?

[sltungle]

Okay, this is a long post so buckle up (not sure if this counts as Homework Help or not - technically it WAS homework, but now it's basically exam revision).

I was wondering if anyone would mind helping me with a few physics problems I have? It was originally for a mastering physics assignment due last Monday, but I didn't get around to finishing all of the problems and now I want to understand how to do them for my upcoming physics exam.

Normally I wouldn't require this great a deal of help - I'm normally incredibly good at physics, I even managed to get high distinctions in our physics course last semester which covered optics, quantum mechanics, and special relativity. Unfortunately thermodynamics seems to be tripping me up a bit, though.

Some of the problems I had in Mastering Physics are as follows:

Question 1

At what pressure ratio would a heat engine operating with a Brayton cycle have an efficiency of 80.0? Assume that the gas is diatomic.

I tried going:

Efficiency = 1 - Qc/Qh, or 1 - Tc/Th with efficiency as 0.80, and then subbing in (pV/nR)cold and (pV/nR)hot for Tc/h but I'm not sure I approaching the problem right. I didn't finish this question.

Question 2

A Carnot refrigerator operating between -20.0 deg and 30.0 degrees Celsius extracts heat from the cold reservoir at the rate 100 J/s. What are (a) the coefficient of performance of this refrigerator, (b) the rate at which work is done on the refrigerator and (c) the rate at which heat is exhausted to the hot side?

What is the coefficient of performance of this refrigerator?
5.06
Correct

What is the rate at which work is done on the refrigerator?
Exhausted 3 of 4 attempts for this question. Can't remember my working unfortunately.

What is the rate at which heat is exhausted to the hot side?
Used 1 of 4 attempts.

This entire question is making me angry at myself. I've always been good at physics but just messing this whole last mastering physics up demoralized me greatly. Any help on any of the problems for that question would be greatly appreciated.

Question 3

250 ml of water at 20.0 degrees Celsius is placed in the freezer compartment of a refrigerator with a coefficient of performance of 4.00. How much heat energy is exhausted into the room as the water is changed to ice at -20.0 degrees Celsius?

Got 0% for that problem. Tried using Q = mcΔT with ΔT as both 40 degrees AND 20 degrees and then relating it to COP = Qc/Qh-Qc, but that got me nowhere. Help on working through it would be appreciated.

Question 4

The power output of a car engine running at 3000 rpm is 500 kW.

How much work is done per cycle if the engine's thermal efficiency is 40.0?Give your answer in kJ.
10.0 kJ
Correct

How much heat is exhausted per cycle if the engine's thermal efficiency is 40.0?Give your answer in kJ.

Gave this one an attempt but didn't get it right

Despite having got the first answer correct (10.0 kJ), upon explaining to a friend how to work through the same problem he used the exact same steps as myself (with different values of course) and Mastering Physics said his answer was wrong. I'm a bit concerned that I fluked the answer after that. My steps were:

1) Convert 3000 rpm to cycles per second (3000/60 = 50 cycles/sec or 50 rps if you will).

2) Divide the output (500 kW or 500 kJ/s) by how many cycles there are per second (which when I look at the units should equal kJ/cycle).

Again - I got the question correct with these two steps, my friend got it wrong.

Sorry for the long post. I'd be happy for any help at all, even if its only one one sub question.

 

[sltungle]

Anyone? Like I said, even help with one of the sub questions would be really appreciated (especially the last one - I can't see why I got it correct, but my friend didn't).

 

[Andrew Mason]

Question 1

Efficiency = 1 - Qc/Qh, or 1 - Tc/Th with efficiency as 0.80, and then subbing in (pV/nR)cold and (pV/nR)hot for Tc/h but I'm not sure I approaching the problem right. I didn't finish this question.

Look up the equation for the efficiency of an ideal Brayton cycle. Set that to .8 and determine what P2/P1 is (using $\gamma=C_p/C_v = ??$ for a diatomic gas such as air).

Question 2

b)Use COP = Qc/W (= Tc/(Th - Tc) = 253/50 = 5.06)

If Qc = 100 J/s what is W?

c) Since W = Qh-Qc, what is Qh? (using the W you determined in b))

Question 3

Got 0% for that problem. Tried using Q = mcΔT with ΔT as both 40 degrees AND 20 degrees and then relating it to COP = Qc/Qh-Qc, but that got me nowhere. Help on working through it would be appreciated.

You have to take into account the latent heat of fusion of water and the heat capacity of ice (it is different than the heat capacity of liquid water).

Question 4

You have found the work per cycle, W. Efficiency = output/input = W/Qh

So if efficiency = .4 what is Qh?

AM