Question: Suppose a heat pump has a stationary bicycle attachment that allows you to provide the work instead of using an electrical wall outlet. If your heat pump has a coefficient of performance of 2.0 and you can cycle at a racing pace (Table 15–2) for a half hour, how much heat can you provide?

The coefficient of performance of a heat pump can be calculated by dividing the heat intake by the pump by the work performed by the pump.

The coefficient of performance of the pump is \({\rm{COP}} = {\rm{2}}{\rm{.0}}\).

From table 15-2, the metabolic rate for bicycling is \(1270\;{{\rm{J}} \mathord{\left/{\vphantom {{\rm{J}} {\rm{s}}}} \right.} {\rm{s}}}\).

The work input to the heat pump is calculated below:

\(\begin{aligned}{l}W &= \left( {1270\;{{\rm{J}} \mathord{\left/{\vphantom {{\rm{J}} {\rm{s}}}} \right.} {\rm{s}}}} \right)\left( {0.5\;{\rm{h}}} \right)\left( {\frac{{3600\;{\rm{s}}}}{{1\;{\rm{h}}}}} \right)\\W &= 2.286 \times {10^6}\;{\rm{J}}\end{aligned}\)

The heat delivered to the heat pump is calculated below:

\(\begin{aligned}{l}{Q_{\rm{H}}} &= W\left( {{\rm{COP}}} \right)\\{Q_{\rm{H}}} &= \left( {2.286 \times {{10}^6}\;{\rm{J}}} \right)\left( {2.0} \right)\\{Q_{\rm{H}}} &= 4.572 \times {10^6}\;{\rm{J}}\end{aligned}\)

Thus, the heat delivered to the heat pump is \(4.572 \times {10^6}\;{\rm{J}}\).