Does refrigerator heat transfer violate the Clausius statement?

[neelakash]

Homework Statement

In the operation of of a refrigerator there is a heat flow out of the reservoir at a lower temperature and a heat flow into a 2nd reservoir at a higher temperature.Explain why this process does not violate the Clausius statement of 2nd law.

Homework Equations

The Attempt at a Solution

My attempts:Please check and confirm if I am correct

Because WORK is being done by the refrigerator compressor to
accomplish this transfer from Tcold to Thot. The Clausius statement
only prohibits heat flow from Tcold to Thot when NO WORK is being
done to enable the transfer.

 

[siddharth]

Yes. The work is provided by the motor in the compressor.