College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![### Heat Calculation Problem
Luis and Salman are trying to increase the temperature of a substance by heating it. What is the quantity of heat in kiloJoules required to raise the temperature of 3.2 kg of the substance from 1°C to 115°C at a pressure of 1.0 atm? Please keep three significant figures.
#### Useful Information:
- **Melting Point:** 293 K
- **Heat of Fusion:** \(3.90 \times 10^4 \, \text{J/kg}\)
- **Boiling Point:** 423 K
- **Heat of Vaporization:** \(7.80 \times 10^4 \, \text{J/kg}\) (at a pressure of 1.0 atm)
- **Specific Heat Capacities:**
- Solid Phase: 600 J/(kg·K)
- Liquid Phase: 1000 J/(kg·K)
- Gaseous Phase: 400 J/(kg·K)
#### Problem Breakdown:
To solve this problem, we will need to consider the various phases and phase transitions of the substance from 1°C to 115°C, and calculate the heat for each step:
1. Heating the solid from 1°C to its melting point of 293 K.
2. Melting the solid at 293 K.
3. Heating the liquid from 293 K to its boiling point of 423 K.
4. Vaporizing the liquid at 423 K.
5. Heating the gas from 423 K to 115°C (388 K).
Let's calculate the energy required for each step as follows:
1. **Heating the solid (1°C to 293 K):**
\[
Q_1 = m \cdot c_{\text{solid}} \cdot \Delta T
\]
Where
\[
\Delta T_1 = 293\,K - 274.15\,K = 18.85\,K
\]
\[
Q_1 = 3.2\,kg \times 600\,\text{J/(kg·K)} \times 18.85\,K = 36,192\,\text{J} = 36.2\,kJ
\]
2. **Melting the solid at 293 K:**
\[
Q_2 = m \cdot \text{heat of fusion](https://content.bartleby.com/qna-images/question/e21b1804-353f-4ea4-b68e-2aafa672ffde/46aa8c7d-2663-400e-9795-c4c4a76c2de1/20ufni_processed.jpeg)
Transcribed Image Text:### Heat Calculation Problem
Luis and Salman are trying to increase the temperature of a substance by heating it. What is the quantity of heat in kiloJoules required to raise the temperature of 3.2 kg of the substance from 1°C to 115°C at a pressure of 1.0 atm? Please keep three significant figures.
#### Useful Information:
- **Melting Point:** 293 K
- **Heat of Fusion:** \(3.90 \times 10^4 \, \text{J/kg}\)
- **Boiling Point:** 423 K
- **Heat of Vaporization:** \(7.80 \times 10^4 \, \text{J/kg}\) (at a pressure of 1.0 atm)
- **Specific Heat Capacities:**
- Solid Phase: 600 J/(kg·K)
- Liquid Phase: 1000 J/(kg·K)
- Gaseous Phase: 400 J/(kg·K)
#### Problem Breakdown:
To solve this problem, we will need to consider the various phases and phase transitions of the substance from 1°C to 115°C, and calculate the heat for each step:
1. Heating the solid from 1°C to its melting point of 293 K.
2. Melting the solid at 293 K.
3. Heating the liquid from 293 K to its boiling point of 423 K.
4. Vaporizing the liquid at 423 K.
5. Heating the gas from 423 K to 115°C (388 K).
Let's calculate the energy required for each step as follows:
1. **Heating the solid (1°C to 293 K):**
\[
Q_1 = m \cdot c_{\text{solid}} \cdot \Delta T
\]
Where
\[
\Delta T_1 = 293\,K - 274.15\,K = 18.85\,K
\]
\[
Q_1 = 3.2\,kg \times 600\,\text{J/(kg·K)} \times 18.85\,K = 36,192\,\text{J} = 36.2\,kJ
\]
2. **Melting the solid at 293 K:**
\[
Q_2 = m \cdot \text{heat of fusion
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