9.7 ### Problem Description**Scenario:** A copper rod has a length of 1.1 meters and a cross-sectional area of \(4.5 \times 10^{-4}\) square meters. One end of the rod is in contact with boiling water, and the other end is in contact with a mixture of ice and water.**Question:** What is the mass of ice that melts per second? Assume that no heat is lost through the side surface of the rod.**Data Entry:** There is a field labeled "m/t =" for entering a value, accompanied by a selection box, likely for units or additional details.### ExplanationThis problem requires applying principles of thermal conduction and phase change. Specifically, you will need to:- Use the formula for heat transfer through conduction: \( Q = \frac{k \cdot A \cdot \Delta T \cdot t}{L} \) - \( k \) is the thermal conductivity of copper. - \( A \) is the cross-sectional area. - \( \Delta T \) is the temperature difference. - \( t \) is time. - \( L \) is the length of the rod.- Calculate the amount of energy used in melting ice using its latent heat of fusion: \( Q = m \cdot L_f \) - \( m \) is the mass of ice melted. - \( L_f \) is the latent heat of fusion for ice.By equating these two expressions for \( Q \) and solving for the mass of ice that melts per second, you can determine the desired value.

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A copper rod has a length of 1.1 m and a cross-sectional area of 4.5 x 10-4 m². One end of the rod is in contact with boiling water and the other with a mixture of ice and water. What is the mass of ice per second that melts? Assume that no heat is lost through the side surface of the rod. m/t = i

A copper rod has a length of 1.1 m and a cross-sectional area of 4.5 x 10-4 m². One end of the rod is in contact with boiling water and the other with a mixture of ice and water. What is the mass of ice per second that melts? Assume that no heat is lost through the side surface of the rod. m/t = i

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Energy transfer

The flow of energy from one region to another region is referred to as energy transfer. Since energy is quantitative; it must be transferred to a body or a material to work or to heat the system.

Molar Specific Heat

Heat capacity is the amount of heat energy absorbed or released by a chemical substance per the change in temperature of that substance. The change in heat is also called enthalpy. The SI unit of heat capacity is Joules per Kelvin, which is (J K-1)

Thermal Properties of Matter

Thermal energy is described as one of the form of heat energy which flows from one body of higher temperature to the other with the lower temperature when these two bodies are placed in contact to each other. Heat is described as the form of energy which is transferred between the two systems or in between the systems and their surrounding by the virtue of difference in temperature. Calorimetry is that branch of science which helps in measuring the changes which are taking place in the heat energy of a given body.

Question

9.7

### Problem Description

**Scenario:**
A copper rod has a length of 1.1 meters and a cross-sectional area of \(4.5 \times 10^{-4}\) square meters. One end of the rod is in contact with boiling water, and the other end is in contact with a mixture of ice and water.

**Question:**
What is the mass of ice that melts per second? Assume that no heat is lost through the side surface of the rod.

**Data Entry:**
There is a field labeled "m/t =" for entering a value, accompanied by a selection box, likely for units or additional details.

### Explanation

This problem requires applying principles of thermal conduction and phase change. Specifically, you will need to:

- Use the formula for heat transfer through conduction: \( Q = \frac{k \cdot A \cdot \Delta T \cdot t}{L} \)
- \( k \) is the thermal conductivity of copper.
- \( A \) is the cross-sectional area.
- \( \Delta T \) is the temperature difference.
- \( t \) is time.
- \( L \) is the length of the rod.

- Calculate the amount of energy used in melting ice using its latent heat of fusion: \( Q = m \cdot L_f \)
- \( m \) is the mass of ice melted.
- \( L_f \) is the latent heat of fusion for ice.

By equating these two expressions for \( Q \) and solving for the mass of ice that melts per second, you can determine the desired value.

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