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 from1° 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 x 104 J/kg. boiling point is 423 K heat of vaporization 7.80 x 104 J/kg (at a pressure of 1.0 atm). The cp 2001/11 14
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.
![### 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe21b1804-353f-4ea4-b68e-2aafa672ffde%2F46aa8c7d-2663-400e-9795-c4c4a76c2de1%2F20ufni_processed.jpeg&w=3840&q=75)
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