Video: Determining the Entropy Change due to Cooling

2.00 × 10² joules of heat is removed from a heat reservoir at a temperature of 2.00 × 10² K. What is the entropy change of the reservoir?

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Video Transcript

2.00 times 10 to the power of two joules of heat is removed from a heat reservoir at a temperature of 2.00 times 10 to the power of two Kelvin. What is the entropy change of the reservoir?

Okay, so in this question, we’ve been asked to find the entropy change of a reservoir when some amount of heat is removed from that reservoir. To do this, we can recall that the entropy change of a system, 𝑑𝑆, is defined as the heat transferred to the system, 𝑑𝑄, divided by the temperature at which this process occurs, 𝑇.

Now the key thing to remember is that 𝑑𝑄 is defined as the heat transferred to a system. But in this case we’ve got a reservoir as our system and heat is removed from the reservoir. So if we know that 2.00 times 10 to the power of two joules of heat is removed from the reservoir, then we know that the value of 𝑑𝑄 is going to be negative. In other words, we have negative 2.00 times 10 to the power of two joules added to the reservoir or we have 2.00 times 10 to the power of two joules removed from the reservoir.

And as well as this, we’ve also been told that this process occurs at a temperature of 2.00 times 10 to the power of two Kelvin. From this information then, we can work out the change in entropy of the reservoir. We can say that 𝑑𝑆, the change in entropy, is equal to negative 2.00 times 10 to the power of two joules, which is 𝑑𝑄, divided by 2.00 times 10 to the power of two Kelvin, which is 𝑇.

Then when we evaluate the fraction on the right-hand side, we find that the change in entropy of the reservoir ends up being negative 1.00 joules per Kelvin. And we have to remember to give this answer to three significant figures, because the quantities that we’ve been given in the question have also been given to us to three significant figures.

Both 2.00 times 10 to the power of two joules and 2.00 times 10 to the power of two Kelvin are to three significant figures. And hence at this point, we have the final answer to our question: the entropy change of the reservoir is negative 1.00 joules per Kelvin.

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