Final answer:
The correct calculations yield a hot reservoir temperature (Th) of 750 K and the final cold reservoir temperature (Tc) of 337.5 K for the stated efficiencies of the Carnot engine; none of the provided options match these results.
Step-by-step explanation:
The question is about finding the initial and final temperatures of the hot and cold reservoirs of a Carnot engine. For a Carnot engine with an efficiency (η) of 0.60, we know from thermodynamics that η = 1 - (Tc/Th). Here Tc and Th are the absolute temperatures of the cold and hot reservoirs, respectively. Given that Tc initially is 27°C, i.e., Tc = 300 K (since we need to convert from Celsius to Kelvin by adding 273), we can rearrange the equation to solve for Th: Th = Tc / (1 - η).
With the given efficiency of 0.60, the equation becomes Th = 300 K / (1 - 0.60) = 300 K / 0.40 = 750 K. Therefore, the constant value of Th is 750 K.
When the efficiency drops to 0.55, the same process can be repeated to find the new Tc using the unchanged value of Th: η = 1 - (Tc/750 K) gives Tc = 750 K * (1 - 0.55) = 337.5 K.
To answer the student's question, (a) the constant value of Th is 750 K, which is not present in the given options; (b) the final value of Tc is 337.5 K. Hence, none of the provided options (a, b, c, d) correspond to the correct calculation based on the given efficiencies.