---
title: "A student places a sample of an unknown metal with a mass of \\(100.0\\text{ g}\\) and an initial temperature of \\(80.0^\\circ\\text{C}\\) into an insulated cup containing \\(50.0\\text{ g}\\) of water at an initial temperature of \\(20.0^\\circ\\text{C}\\). The specific heat capacity of the metal is \\(0.42\\text{ J/(g}\\cdot^\\circ\\text{C)}\\), and the specific heat capacity of water is \\(4.2\\text{ J/(g}\\cdot^\\circ\\text{C)}\\). Assuming no heat is lost to the surroundings or the cup, what is the final thermal equilibrium temperature of the system?"
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url: "https://nerd-notes.com/ubq/119284/"
date_modified: "2026-08-19T12:39:39+00:00"
---

# A student places a sample of an unknown metal with a mass of \(100.0\text{ g}\) and an initial temperature of \(80.0^\circ\text{C}\) into an insulated cup containing \(50.0\text{ g}\) of water at an initial temperature of \(20.0^\circ\text{C}\). The specific heat capacity of the metal is \(0.42\text{ J/(g}\cdot^\circ\text{C)}\), and the specific heat capacity of water is \(4.2\text{ J/(g}\cdot^\circ\text{C)}\). Assuming no heat is lost to the surroundings or the cup, what is the final thermal equilibrium temperature of the system?

A student places a sample of an unknown metal with a mass of \(100.0\text{ g}\) and an initial temperature of \(80.0^\circ\text{C}\) into an insulated cup containing \(50.0\text{ g}\) of water at an initial temperature of \(20.0^\circ\text{C}\). The specific heat capacity of the metal is \(0.42\text{ J/(g}\cdot^\circ\text{C)}\), and the specific heat capacity of water is \(4.2\text{ J/(g}\cdot^\circ\text{C)}\). Assuming no heat is lost to the surroundings or the cup, what is the final thermal equilibrium temperature of the system?

- **A.** \(24.0^\circ\text{C}\)
- **B.** \(26.0^\circ\text{C}\)
- **C.** \(30.0^\circ\text{C}\)
- **D.** \(50.0^\circ\text{C}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/119284/*