Question

For a Carnot refrigerator operating between \(40^\circ C\) and \(25^\circ C\), the coefficient of performance is

• A. \(39.74\)
• B. \(19.88\)
• C. \(1.97\)
• D. \(5.87\)

Hint:

For Carnot refrigerator, use \(COP=\frac{T_L}{T_H-T_L}\). Always convert Celsius into Kelvin.

Answer 1

The Correct Option is B

For a Carnot refrigerator, coefficient of performance is: \[ COP=\frac{T_L}{T_H-T_L} \] where, \[ T_L=\text{lower temperature} \] and \[ T_H=\text{higher temperature} \] The refrigerator operates between: \[ 40^\circ C \] and \[ 25^\circ C \] Convert temperatures into Kelvin: \[ T_H=40+273=313K \] \[ T_L=25+273=298K \] Now apply the formula: \[ COP=\frac{298}{313-298} \] \[ COP=\frac{298}{15} \] \[ COP=19.86 \] The nearest option is: \[ 19.88 \] Therefore, the coefficient of performance is: \[ 19.88 \]