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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### 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.
Transcribed Image Text:### 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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