Question

A refrigerating machine working on a reversed Carnot cycle takes out 2 kW of heat from the system while working between temperature limits of 300K and 200K. The coefficient of performance and power consumed by the cycle will be respectively:

• A. 1 and 1 kW
• B. 2 and 1 kW
• C. 1 and 2 kW
• D. 2 and 2 kW

Hint:

To calculate the speed corresponding to a given Mach number, use the formula \( v = M \times c \), where \( c \) is the speed of sound calculated using \( c = \sqrt{k R T} \).

Answer 1

The Correct Option is B

Step 1: COP Formula for a Carnot Cycle
The Coefficient of Performance (COP) for a reversed Carnot cycle is defined as:\[\text{COP} = \frac{Q_L}{W} = \frac{T_L}{T_H - T_L}\]Where:- \( Q_L \) represents the heat extracted from the cold reservoir (2 kW),- \( T_L \) is the cold reservoir's temperature (200 K),- \( T_H \) is the hot reservoir's temperature (300 K).Step 2: COP Calculation
Substitute \( T_L \) and \( T_H \) into the COP formula:\[\text{COP} = \frac{200}{300 - 200} = \frac{200}{100} = 2\]Therefore, the COP equals 2.Step 3: Power Consumption Calculation (W)
The power consumed by the refrigeration machine is calculated using the following relation:\[W = \frac{Q_L}{\text{COP}} = \frac{2 \, \text{kW}}{2} = 1 \, \text{kW}\] Final Answer:\[\boxed{2 \, \text{and} \, 1 \, \text{kW}}\]