Final answer:
To find the entropy change in a hot reservoir, divide the heat transferred out of the reservoir by its constant temperature, ensuring to use a negative sign for the heat since it is leaving the reservoir.
Step-by-step explanation:
The question asks us to calculate the entropy change in a hot reservoir, specifically within the context of a Carnot engine cycle. In thermodynamics, entropy is a measure of the disorder or randomness of a system.
When heat Qh is transferred out of a hot reservoir at a constant temperature Th, the entropy decrease of the hot reservoir is given by
. It is important to note that Qh is negative in this context because heat is leaving the reservoir. For a given amount of heat Qh, and reservoir temperature Th, we can calculate the change in entropy for a hypothetical reversible process, which applies equally for an irreversible process.
For example, if 4000 J of heat transfer occurs from a hot reservoir at Th = 600 K to a cold reservoir at Tc = 250 K, we can calculate the change in entropy for the hot reservoir by dividing the heat transferred by the temperature of the hot reservoir. This would be ΔSh = -4000 J/600 K, resulting in an entropy change of -6.67 J/K for the hot reservoir.