---
title: "An insulated container holds a mass \\(m\\) of a liquid with specific heat capacity \\(c\\). In Experiment 1, a mechanical paddle wheel does work \\(W\\) on the liquid by stirring it. In Experiment 2, an identical sample of the liquid in an insulated container receives heat \\(Q = W\\) from a submerged heating wire with no stirring. How does the temperature change \\(\\Delta T_1\\) of the liquid in Experiment 1 compare to the temperature change \\(\\Delta T_2\\) of the liquid in Experiment 2, and why?"
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url: "https://nerd-notes.com/ubq/116264/"
date_modified: "2026-08-03T11:46:32+00:00"
---

# An insulated container holds a mass \(m\) of a liquid with specific heat capacity \(c\). In Experiment 1, a mechanical paddle wheel does work \(W\) on the liquid by stirring it. In Experiment 2, an identical sample of the liquid in an insulated container receives heat \(Q = W\) from a submerged heating wire with no stirring. How does the temperature change \(\Delta T_1\) of the liquid in Experiment 1 compare to the temperature change \(\Delta T_2\) of the liquid in Experiment 2, and why?

An insulated container holds a mass \(m\) of a liquid with specific heat capacity \(c\). In Experiment 1, a mechanical paddle wheel does work \(W\) on the liquid by stirring it. In Experiment 2, an identical sample of the liquid in an insulated container receives heat \(Q = W\) from a submerged heating wire with no stirring. How does the temperature change \(\Delta T_1\) of the liquid in Experiment 1 compare to the temperature change \(\Delta T_2\) of the liquid in Experiment 2, and why?

![Side-by-side comparison of two identical insulated containers filled with liquid. Experiment 1 on the left shows a vertical rotating shaft entering through a top seal, terminating in a submerged paddle wheel with a label W entering along the shaft. Experiment 2 on the right shows an electrical heating element submerged in the liquid, connected to external leads, with a label Q entering the coil. Both containers feature double-walled hatching indicating thermal insulation. No other text or labels appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785757592-xU1WlG.jpg)

- **A.** \(\Delta T_1 > \Delta T_2\) because mechanical stirring increases the macroscopic kinetic energy of the fluid in addition to increasing thermal energy.
- **B.** \(\Delta T_1 < \Delta T_2\) because mechanical work is less efficient than heat transfer at increasing the internal energy of a liquid.
- **C.** \(\Delta T_1 = \Delta T_2\) because work done on a system and heat added to a system both increase the internal energy \(\Delta U\) by the same amount.
- **D.** \(\Delta T_1 = \Delta T_2\) because mechanical work performed on a liquid must be converted into heat before it can change the temperature.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116264/*