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: Formula for Coefficient of Performance (COP) of a Carnot cycle
For a reversed Carnot cycle, the Coefficient of Performance (COP) is given by: \[ \text{COP} = \frac{Q_L}{W} = \frac{T_L}{T_H - T_L} \] Where: - \( Q_L \) is the heat removed from the cold reservoir (2 kW in this case), - \( T_L \) is the temperature of the cold reservoir (200 K), - \( T_H \) is the temperature of the hot reservoir (300 K). Step 2: Calculate COP
Substitute the values of \( T_L \) and \( T_H \) into the formula: \[ \text{COP} = \frac{200}{300 - 200} = \frac{200}{100} = 2 \] So, the COP is 2. Step 3: Calculate the power consumed (W)
The power consumed by the refrigerating machine is related to the heat removed and the COP: \[ W = \frac{Q_L}{\text{COP}} = \frac{2 \, \text{kW}}{2} = 1 \, \text{kW} \] Final Answer: \[ \boxed{2 \, \text{and} \, 1 \, \text{kW}} \]