1.900 x 106 J of heat is added to a cylinder of aluminum (radius 5.000 cm, length 10.00 cm) at room temperature (let's call the temperature exactly 300 K). Is this amount of heat enough to completely melt the aluminum? Assume the specific heat quoted in the text applies to aluminum in any phase and also that the density is valid at 300 K. 1) Calculate the mass of the aluminum sample. 2) What would be the AT for this sample if it was raised to the the phase boundary between the solid and liquid states of matter? Ignore, for now, whether this amount of heat is actually enough to make that happen. 3) Look up the specific heat for this sample and report it in course standard units, Hint: what are the standard units of energy, mass, and which are E [m}{T] * temperature? 4) Look up the latent heat of fusion for this sample and report it in standard units, which are (m]
1.900 x 106 J of heat is added to a cylinder of aluminum (radius 5.000 cm, length 10.00 cm) at room temperature (let's call the temperature exactly 300 K). Is this amount of heat enough to completely melt the aluminum? Assume the specific heat quoted in the text applies to aluminum in any phase and also that the density is valid at 300 K. 1) Calculate the mass of the aluminum sample. 2) What would be the AT for this sample if it was raised to the the phase boundary between the solid and liquid states of matter? Ignore, for now, whether this amount of heat is actually enough to make that happen. 3) Look up the specific heat for this sample and report it in course standard units, Hint: what are the standard units of energy, mass, and which are E [m}{T] * temperature? 4) Look up the latent heat of fusion for this sample and report it in standard units, which are (m]
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Can you please do only 4. thank you
![**Title: Heat Transfer in an Aluminum Cylinder**
**Introduction:**
This exercise explores the heat transfer dynamics in a cylindrical aluminum sample when a specific amount of heat is added. The objective is to understand if the applied heat is sufficient to completely melt the aluminum.
Given Data:
- Heat added: \(1.900 \times 10^6 \text{ J}\)
- Aluminum cylinder dimensions:
- Radius: 5.000 cm
- Length: 10.00 cm
- Room temperature: 300 K (assumed exact)
- Specific heat and density of aluminum are assumed to be constant across all phases at 300 K.
**Tasks:**
1. **Calculate the mass of the aluminum sample.**
2. **Determine the temperature change (\(\Delta T\)) for the sample if it reaches the phase boundary between solid and liquid states. For now, ignore whether this amount of heat is sufficient to induce this change.**
3. **Identify the specific heat (\(c\)) for the aluminum sample and express it in standard course units, \(\left[ \frac{E}{m[T]} \right]\).**
Hint: Consider the standard units of energy (E), mass (m), and temperature (T).
4. **Identify the latent heat of fusion for the aluminum sample and report it in standard units, \(\left[ \frac{E}{m} \right]\).**
**Explanation:**
The questions provided in this problem set aim to use principles of thermodynamics to evaluate the thermal properties and behavior of aluminum when subjected to heat.
1. **Calculate the Mass:**
- The mass of the aluminum cylinder can be calculated using the formula for the volume of a cylinder \(V = \pi r^2 h\) and the density \(\rho\) of aluminum:
\[
V = \pi (0.05 \, \text{m})^2 (0.1 \, \text{m})
\]
\[
m = \rho V
\]
The density value \(\rho\) for aluminum must be looked up or given as part of the problem.
2. **Determine \(\Delta T\):**
- Using the relationship \(Q = mc\Delta T\):
\[
\Delta T = \frac{Q}{mc}
\]
- Here, \(Q\) is the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9db2ddca-93d8-4ce7-b35d-4c5475f9bef7%2F16da79af-e48f-4550-af14-403d815cc364%2F3wykujv_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Heat Transfer in an Aluminum Cylinder**
**Introduction:**
This exercise explores the heat transfer dynamics in a cylindrical aluminum sample when a specific amount of heat is added. The objective is to understand if the applied heat is sufficient to completely melt the aluminum.
Given Data:
- Heat added: \(1.900 \times 10^6 \text{ J}\)
- Aluminum cylinder dimensions:
- Radius: 5.000 cm
- Length: 10.00 cm
- Room temperature: 300 K (assumed exact)
- Specific heat and density of aluminum are assumed to be constant across all phases at 300 K.
**Tasks:**
1. **Calculate the mass of the aluminum sample.**
2. **Determine the temperature change (\(\Delta T\)) for the sample if it reaches the phase boundary between solid and liquid states. For now, ignore whether this amount of heat is sufficient to induce this change.**
3. **Identify the specific heat (\(c\)) for the aluminum sample and express it in standard course units, \(\left[ \frac{E}{m[T]} \right]\).**
Hint: Consider the standard units of energy (E), mass (m), and temperature (T).
4. **Identify the latent heat of fusion for the aluminum sample and report it in standard units, \(\left[ \frac{E}{m} \right]\).**
**Explanation:**
The questions provided in this problem set aim to use principles of thermodynamics to evaluate the thermal properties and behavior of aluminum when subjected to heat.
1. **Calculate the Mass:**
- The mass of the aluminum cylinder can be calculated using the formula for the volume of a cylinder \(V = \pi r^2 h\) and the density \(\rho\) of aluminum:
\[
V = \pi (0.05 \, \text{m})^2 (0.1 \, \text{m})
\]
\[
m = \rho V
\]
The density value \(\rho\) for aluminum must be looked up or given as part of the problem.
2. **Determine \(\Delta T\):**
- Using the relationship \(Q = mc\Delta T\):
\[
\Delta T = \frac{Q}{mc}
\]
- Here, \(Q\) is the
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