Is 600J the Minimum Heat Transfer to Maintain Entropy in a Thermodynamic Cycle?

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Bigfoots mum
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Hi, i just want to check my reasoning on this problem.

A working substance is taken around a closed cycle that involves performing some external work. It absorbes heat Q1 = 1000J from a resevoir at T1 = 1000K, and heat Q2 = 2000J from a resevoir at T2 =2000K. The only other exchange of heat is with a resevoir at T3 = 300K.
What is the minimum heat that must have been transferred from the substance to the resevoir at T3 ( explain your reasoning)?

Now i think the minimum heat is 600J, as the entropy change of the system must be >= 0, and we must have heat rejection otherwise we'd violate the 2nd law. Is this ok?
Thanks
 
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Hi Bigfoots mum, welcome to PF. Your reasoning looks good to me.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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