How many kilojoules of energy are needed to convert 105 g of ice at -17.0 to water at 22.4°C? (The specific heat of ice at -17.0 is 2.01 J/g°C.)
How many kilojoules of energy are needed to convert 105 g of ice at -17.0 to water at 22.4°C? (The specific heat of ice at -17.0 is 2.01 J/g°C.)
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Question
How many kilojoules of energy are needed to convert 105 g of ice at -17.0 to water at 22.4°C? (The specific heat of ice at -17.0 is 2.01 J/g°C.)
![**Problem Statement:**
How many kilojoules of energy are needed to convert 105 g of ice at -17.0°C to water at 22.4°C? (The specific heat of ice at -17.0°C is 2.01 J/g°C.)
[Input Field] kJ
*Note:* The number of significant digits is set to 3; the tolerance is +/-2%.
**Explanation:**
In this problem, you'll need to calculate the total energy required to convert ice at a sub-zero temperature to water at room temperature. This involves considering both the heating of ice to 0°C, the phase change from ice to water at 0°C, and finally heating the resulting water to the desired temperature. The calculations typically involve:
1. **Heating the Ice:**
Use the specific heat capacity to calculate the energy required to raise the temperature of ice from -17.0°C to 0°C.
\[
q_1 = m \cdot c \cdot \Delta T
\]
Where \( q_1 \) is the heat energy, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.
2. **Melting the Ice:**
Calculate the energy needed for the phase change from ice to water using the heat of fusion.
3. **Heating the Water:**
Calculate the energy required to raise the temperature of water from 0°C to 22.4°C.
Finally, convert the total energy from joules to kilojoules and express your answer with the specified number of significant figures and tolerance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdfb5e0e0-201d-4cf8-afd1-44e158f05a1a%2F57159aa4-e0b8-41c1-bb85-8d4663ecdcef%2Fc5hef2g_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
How many kilojoules of energy are needed to convert 105 g of ice at -17.0°C to water at 22.4°C? (The specific heat of ice at -17.0°C is 2.01 J/g°C.)
[Input Field] kJ
*Note:* The number of significant digits is set to 3; the tolerance is +/-2%.
**Explanation:**
In this problem, you'll need to calculate the total energy required to convert ice at a sub-zero temperature to water at room temperature. This involves considering both the heating of ice to 0°C, the phase change from ice to water at 0°C, and finally heating the resulting water to the desired temperature. The calculations typically involve:
1. **Heating the Ice:**
Use the specific heat capacity to calculate the energy required to raise the temperature of ice from -17.0°C to 0°C.
\[
q_1 = m \cdot c \cdot \Delta T
\]
Where \( q_1 \) is the heat energy, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.
2. **Melting the Ice:**
Calculate the energy needed for the phase change from ice to water using the heat of fusion.
3. **Heating the Water:**
Calculate the energy required to raise the temperature of water from 0°C to 22.4°C.
Finally, convert the total energy from joules to kilojoules and express your answer with the specified number of significant figures and tolerance.
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