---
title: "A residential heat pump operates by extracting thermal energy \\(Q_C\\) from cold outdoor air at temperature \\(T_C\\) and delivering thermal energy \\(Q_H\\) to the warm interior of a house at temperature \\(T_H\\). To accomplish this transfer, an electric compressor performs work \\(W\\) on the working fluid during each cycle. Which of the following correctly compares \\(Q_H\\) to \\(W\\) and provides the correct thermodynamic justification?"
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url: "https://nerd-notes.com/ubq/116172/"
date_modified: "2026-08-03T11:46:07+00:00"
---

# A residential heat pump operates by extracting thermal energy \(Q_C\) from cold outdoor air at temperature \(T_C\) and delivering thermal energy \(Q_H\) to the warm interior of a house at temperature \(T_H\). To accomplish this transfer, an electric compressor performs work \(W\) on the working fluid during each cycle. Which of the following correctly compares \(Q_H\) to \(W\) and provides the correct thermodynamic justification?

A residential heat pump operates by extracting thermal energy \(Q_C\) from cold outdoor air at temperature \(T_C\) and delivering thermal energy \(Q_H\) to the warm interior of a house at temperature \(T_H\). To accomplish this transfer, an electric compressor performs work \(W\) on the working fluid during each cycle. Which of the following correctly compares \(Q_H\) to \(W\) and provides the correct thermodynamic justification?

- **A.** \(Q_H < W\), because energy conversion constraints prohibit the heat delivered to a system from exceeding the net mechanical work done on it.
- **B.** \(Q_H = W\), because thermal energy cannot be absorbed from air colder than the house interior, so all heat delivered comes entirely from converted work.
- **C.** \(Q_H > W\), because thermal energy spontaneously flows from colder to warmer regions, so work is only required to overcome mechanical friction in the compressor.
- **D.** \(Q_H > W\), because work must be done to transfer thermal energy from a colder to a warmer environment, and energy conservation requires \(Q_H = Q_C + W\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116172/*