What is the coefficient of performance of an ideal heat pump that extracts heat from 6°C air outside and deposits heat inside a house at 24°C?

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Understand the concept: The coefficient of performance (COP) for a heat pump is a measure of its efficiency. For an ideal heat pump, the COP is given by the formula:

COP = \frac{T_{h}}{T_{h}}

, where

T_{h}

is the temperature of the hot reservoir (inside the house) and

T_{c}

is the temperature of the cold reservoir (outside air).

Convert the temperatures from Celsius to Kelvin: Since the formula requires temperatures in Kelvin, use the conversion

T = t + 273.15

, where

t

is the temperature in Celsius. For the hot reservoir,

T_{h} = 24 + 273.15

. For the cold reservoir,

T_{c} = 6 + 273.15

Substitute the converted temperatures into the COP formula: Replace

T_{h}

and

T_{c}

in the formula

COP = \frac{T_{h}}{T_{h}}

Simplify the expression: Perform the subtraction in the denominator and simplify the fraction to find the COP.

Interpret the result: The COP value represents how many units of heat energy are delivered to the house for each unit of work input. A higher COP indicates a more efficient heat pump.

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주요 개념

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Coefficient of Performance (COP)

The Coefficient of Performance (COP) is a measure of the efficiency of a heat pump, defined as the ratio of heat output to the work input. For heating applications, it is calculated as the heat delivered to the warm space divided by the energy consumed by the pump. A higher COP indicates a more efficient heat pump, meaning it can transfer more heat for each unit of energy consumed.

Heat Pump Operation

A heat pump operates by transferring heat from a cooler area to a warmer area, utilizing the principles of thermodynamics. It absorbs heat from the outside environment (in this case, 6°C air) and releases it indoors (at 24°C). The process involves a refrigerant that circulates through the system, changing states from liquid to gas and back, which allows it to absorb and release heat effectively.

Thermodynamic Temperature Scale

The thermodynamic temperature scale, often measured in Kelvin, is crucial for calculating the efficiency of heat pumps. Temperatures in Celsius must be converted to Kelvin by adding 273.15, as thermodynamic equations require absolute temperatures. This conversion is essential for accurately determining the COP and understanding the energy transfer processes involved in heat pump operation.