Final answer:
The amount of energy absorbed by the cold body when a Carnot heat engine is used as a refrigerator can be calculated using the coefficient of performance (COP), which is based on the temperatures of the cold and hot reservoirs, and the work done on the system.
Step-by-step explanation:
To find the amount of energy absorbed by the cold body when a Carnot heat engine is used as a refrigerator and 10 J of work is done on the system, we use the concept of the coefficient of performance (COP) of a refrigerator. The COP is defined as the amount of heat removed from the cold reservoir (Qc) divided by the work done on the system (W). For a Carnot refrigerator, the COP is also expressed in terms of the temperatures of the hot (Th) and cold (Tc) reservoirs.
The formula for the COP of a Carnot refrigerator is:
COP = Tc / (Th - Tc)
where Tc and Th are the absolute temperatures (in kelvins) of the cold and hot reservoirs, respectively. To convert the temperatures from Celsius to Kelvin, we add 273 to the Celsius temperatures. Assuming the given temperatures for a typical problem: if the refrigerator is operating between -10 °C (263 K) and 30 °C (303 K), and we are given the work W = 10J, we can calculate the energy absorbed by the cold body using:
Qc = COP × W
First, calculate the COP with the temperatures provided, then multiply by the work done (10J) to find Qc. Remember that in any real-world application, the actual refrigerator would likely not be as efficient as the idealized Carnot refrigerator due to practical limitations.