# Homework Help: Min power needed to maintain a sample at given temperature

1. Nov 4, 2015

### jdawg

1. The problem statement, all variables and given/known data
A sample in a lab is maintained at a cryogenic temperature of -195 °F. The lab is a balmy 70 °F. Heat leaks into the sample at a known rate, Q leak, which raises the temperature.

Provide a brief explanation of how you would determine the minimum power needed to maintain the sample at -195 °F. Be sure to include relevant equations.

2. Relevant equations

3. The attempt at a solution
I'm a little bit confused about this diagram! I know that HVAC cycles require work, which would make me think this is an HVAC cycle since work is being put into the system. But the rotation is clockwise, which would make me think its a power cycle! Can someone explain to me why the direction of work and rotation are contradicting each other?
Also, when is the power at its minimum? Is it maybe when QH is at its minimum?
(Sorry that the diagram is upside down, I couldn't get it to rotate!)

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2. Nov 5, 2015

### CWatters

I can't comment on the clockwise/anticlockwise issue but does it stop you solving the problem?

QH is the power coming out of the system into the room. You could minimise QH by turning off the heat pump but what would happen to the sample temperature?

3. Nov 5, 2015

### jdawg

I found out that my professor messed up on the diagram and his rotation was wrong. Would the temperature of the sample decrease?

4. Nov 6, 2015

### CWatters

No. What happens to the contents of a fridge if you turn the fridge off :-)

Take a look at the "sample" block on the diagram. What is the condition for constant sample temperature?

QC < QLeak?
QC > QLeak?
QC = QLeak?

5. Nov 6, 2015

### jdawg

Ohh thanks so much!

6. Nov 7, 2015

7. Nov 7, 2015

### jdawg

I think Qc = Qleak?

8. Nov 7, 2015

### CWatters

That's correct but I actually meant your overall answer to the question.