Min power needed to maintain a sample at given temperature

In summary, the problem involves maintaining a sample at a cryogenic temperature in a lab where heat leaks in at a known rate, Q leak, from the surrounding balmy temperature. To determine the minimum power needed to maintain the sample at -195 °F, we can use the equation QC = Q leak, which states that the power going into the sample is equal to the heat leakage. This means that the power at its minimum would be when QH (power coming out of the system) is at its minimum, which can be achieved by turning off the heat pump. However, this would cause the sample temperature to increase. Thus, the condition for constant sample temperature is QC = Q leak.
  • #1
jdawg
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Homework Statement


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.

Homework Equations

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

jdawg said:
Also, when is the power at its minimum? Is it maybe when QH is at its minimum?

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?
 
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  • #3
I found out that my professor messed up on the diagram and his rotation was wrong. Would the temperature of the sample decrease?
 
  • #4
CWatters said:
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?

jdawg said:
Would the temperature of the sample decrease?

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?
 
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  • #5
Ohh thanks so much!
 
  • #6
Care to post your answer?
 
  • #7
I think Qc = Qleak?
 
  • #8
That's correct but I actually meant your overall answer to the question.
 

What is the minimum power needed to maintain a sample at a given temperature?

The minimum power needed to maintain a sample at a given temperature depends on various factors such as the type of sample, its size, and the surrounding environment. It is important to conduct experiments or simulations to determine the specific power needed for a particular sample.

How does the type of sample affect the minimum power needed to maintain it at a given temperature?

The type of sample can greatly affect the minimum power needed to maintain it at a given temperature. For example, a solid sample may require less power compared to a liquid sample due to differences in thermal conductivity. Additionally, the chemical composition of the sample can also impact the power needed for temperature maintenance.

Is there a standard formula for calculating the minimum power needed to maintain a sample at a given temperature?

There is no standard formula for calculating the minimum power needed to maintain a sample at a given temperature. The power needed can vary depending on the specific conditions and parameters of the experiment. However, there are general guidelines and equations that can be used as starting points for determining the power needed.

What are the common methods used to determine the minimum power needed for temperature maintenance?

There are various methods that can be used to determine the minimum power needed for temperature maintenance. Some common methods include conducting experiments with different power inputs and measuring the resulting temperature changes, using mathematical models and simulations, and referencing previously published data or studies on similar samples.

How can the minimum power needed for temperature maintenance be optimized for energy efficiency?

To optimize the minimum power needed for temperature maintenance, it is important to consider factors such as the insulation of the sample, the use of efficient heating or cooling devices, and the optimization of experimental parameters. Additionally, using renewable energy sources and implementing energy-saving techniques can also help to improve energy efficiency.

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