# Step-by-Step Solution: Plotting Heat Transfer and Temperature Change Below is a guide to creating the requested plot. Since the details of "Question " are not provided, I'll describe the **general method** using a typical phase change scenario (e.g., heating ice at \(-10^\circ\)C to steam at \(120^\circ\)C## 1. **Identify Steps in Heating** Let’s assume we have 1. g of ice at \(-10^\circ\)C, and we want to heat it to steam at \(120^\circ\)C. The steps are: 1. **Heat ice from \(-10^\circ\)C to \(^\circ\)C** (solid warms) 2. **Melt ice at \(^\circ\)C** (solid melts) 3. **Heat water from \(^\circ\)C to \(100^\circ\)C** (liquid warms) 4. **Vaporize water at \(100^\circ\)C** (liquid boils) 5. **Heat steam from \(100^\circ\)C to \(120^\circ\)C** (gas warms) ## 2. **Equations & Constants** - \(q = m c \Delta T\) (heating/cooling) - \(q = m \Delta H_\text{fus}\) (melting/freezing) - \(q = m \Delta H_\text{vap}\) (boiling/condensing) Common values for 1. g water: - \(c_\text{ice} = 2.09\,\mathrm{J/g\,^\circ C}\) - \(c_\text{water} = 4.18\,\mathrm{J/g\,^\circ C}\) - \(c_\text{steam} = 2.01\,\mathrm{J/g\,^\circ C}\) - \(\Delta H_\text{fus} = 334\,\mathrm{J/g}\) - \(\Delta H_\text{vap} = 226\,\mathrm{J/g}\) ## 3. **Calculate Heat for Each Step** ### 1. Heating ice (\(-10^\circ\)C to \(^\circ\)C): \[ q_1 = m c_\text{ice} \Delta T = 1. \times 2.09 \times ( - (-10)) = 20.9~\mathrm{J} \] ### 2. Melting ice at \(^\circ\)C: \[ q_2 = m \Delta H_\text{fus} = 1. \times 334 = 334~\mathrm{J} \] ### 3. Heating water (\(^\circ\)C to \(100^\circ\)C): \[ q_3 = m c_\text{water} \Delta T = 1. \times 4.18 \times (100-) = 418~\mathrm{J} \] ### 4. Vaporizing water at \(100^\circ\)C: \[ q_4 = m \Delta H_\text{vap} = 1. \times 226 = 226~\mathrm{J} \] ### 5. Heating steam (\(100^\circ\)C to \(120^\circ\)C): \[ q_5 = m c_\text{steam} \Delta T = 1. \times 2.01 \times (120-100) = 40.2~\mathrm{J} \] ## 4. **Cumulative Heat Values** | Step | Process | Final Temp (\(^\circ\)C) | Cumulative \(q\) (J) | |------|----------------------|--------------------------|----------------------| | 1 | Heat ice | | 20.9 | | 2 | Melt ice | | 354.9 | | 3 | Heat water | 100 | 772.9 | | 4 | Boil water | 100 | 3032.9 | | 5 | Heat steam | 120 | 3073.1 | ## 5. **Plot Construction** - **X-axis:** Heat added (\(q\), in J) - **Y-axis:** Temperature (\(^\circ\)C) **Plot points:** - (, -10) - (20.9, ) - (354.9, ) _(horizontal, melting)_ - (772.9, 100) - (3032.9, 100) _(horizontal, boiling)_ - (3073.1, 120) **Label segments:** - "Solid warms" (\(-10^\circ\)C to \(^\circ\)C) - "Solid melts" (plateau at \(^\circ\)C) - "Liquid warms" (\(^\circ\)C to \(100^\circ\)C) - "Liquid boils" (plateau at \(100^\circ\)C) - "Gas warms" (\(100^\circ\)C to \(120^\circ\)C) ## 6. **Sample Plot** ```plaintext Temperature (^oC) | | _________ | / \ | / \ |_____/ \________ | | +------------------------------------------ Heat added (J) ``` Below is a simple code to create the plot using Python/Matplotlib: ```python import matplotlib.pyplot as plt q = [, 20.9, 354.9, 772.9, 3032.9, 3073.1] T = [-10, , , 100, 100, 120] plt.plot(q, T, marker='o') plt.xlabel('Heat Added (J)') plt.ylabel('Temperature (°C)') plt.title('Temperature vs Heat Added for Heating 1g Ice (-10°C to 120°C)') plt.grid(True) # Annotate segments plt.text(10, -5, 'Solid warms', fontsize=8) plt.text(100, 5, 'Melting', fontsize=8) plt.text(500, 50, 'Liquid warms', fontsize=8) plt.text(200, 105, 'Boiling', fontsize=8) plt.text(305, 115, 'Gas warms', fontsize=8) plt.show() ``` --- ## **Final Answer:** - The plot is a **stepwise graph**: temperature rises linearly with added heat during warming phases, remains **constant (horizontal plateaus)** during phase changes (melting and boiling). - **Label the segments** as "Solid warms", "Melting", "Liquid warms", "Boiling", "Gas warms". - **[Sample plot below]**  *Alt text: Stepwise plot of temperature versus heat added showing solid, melting, liquid, boiling, and gas phases.* > **Note:** For your specific problem, use the actual masses, temperature ranges, and enthalpy values provided in your Question 5. The method remains the same.

# Step-by-Step Solution: Plotting Heat Transfer and Temperature Change This guide provides a general method for creating a plot of heat transfer and temperature change, assuming a system where 1 g of ice at \(-10^\circ\)C is heated to steam at \(120^\circ\)C. ## 1. Identify Steps in Heating The heating process can be divided into five main steps: 1. **Heat ice from \(-10^\circ\)C to \(0^\circ\)C** (solid warms) 2. **Melt ice at \(0^\circ\)C** (solid melts) 3. **Heat water from \(0^\circ\)C to \(100^\circ\)C** (liquid warms) 4. **Vaporize water at \(100^\circ\)C** (liquid boils) 5. **Heat steam from \(100^\circ\)C to \(120^\circ\)C** (gas warms) ## 2. Equations & Constants - **Heating/Cooling**: \(q = m c \Delta T\) - **Melting/Freezing**: \(q = m \Delta H_\text{fus}\) - **Boiling/Condensing**: \(q = m \Delta H_\text{vap}\) ### Constants for 1 g of Water: - \(c_\text{ice} = 2.09\,\mathrm{J/g\,^\circ C}\) - \(c_\text{water} = 4.18\,\mathrm{J/g\,^\circ C}\) - \(c_\text{steam} = 2.01\,\mathrm{J/g\,^\circ C}\) - \(\Delta H_\text{fus} = 334\,\mathrm{J/g}\) - \(\Delta H_\text{vap} = 226\,\mathrm{J/g}\) ## 3. Calculate Heat for Each Step ### Step 1: Heating Ice (\(-10^\circ\)C to \(0^\circ\)C) \[ q_1 = m c_\text{ice} \Delta T = 1 \times 2.09 \times (0 - (-10)) = 20.9~\mathrm{J} \] ### Step 2: Melting Ice at \(0^\circ\)C \[ q_2 = m \Delta H_\text{fus} = 1 \times 334 = 334~\mathrm{J} \] ### Step 3: Heating Water (\(0^\circ\)C to \(100^\circ\)C) \[ q_3 = m c_\text{water} \Delta T = 1 \times 4.18 \times (100 - 0) = 418~\mathrm{J} \] ### Step 4: Vaporizing Water at \(100^\circ\)C \[ q_4 = m \Delta H_\text{vap} = 1 \times 226 = 226~\mathrm{J} \] ### Step 5: Heating Steam (\(100^\circ\)C to \(120^\circ\)C) \[ q_5 = m c_\text{steam} \Delta T = 1 \times 2.01 \times (120 - 100) = 40.2~\mathrm{J} \] ## 4. Cumulative Heat Values | Step | Process | Final Temp (\(^\circ\)C) | Cumulative \(q\) (J) | |------|----------------------|--------------------------|----------------------| | 1 | Heat ice | \(0\) | \(20.9\) | | 2 | Melt ice | \(0\) | \(354.9\) | | 3 | Heat water | \(100\) | \(772.9\) | | 4 | Boil water | \(100\) | \(999.9\) | | 5 | Heat steam | \(120\) | \(1040.1\) | ## 5. Plot Construction - **X-axis:** Heat added (\(q\), in J) - **Y-axis:** Temperature (\(^\circ\)C) ### Plot Points: - (0, -10) - (20.9, 0) - (354.9, 0) _(horizontal, melting)_ - (772.9, 100) - (999.9, 100) _(horizontal, boiling)_ - (1040.1, 120) ### Label Segments: - "Solid warms" (\(-10^\circ\)C to \(0^\circ\)C) - "Solid melts" (at \(0^\circ\)C) - "Liquid warms" (\(0^\circ\)C to \(100^\circ\)C) - "Liquid boils" (at \(100^\circ\)C) - "Gas warms" (\(100^\circ\)C to \(120^\circ\)C) ## 6. Sample Plot Here is a sample code to create the plot using Python/Matplotlib: ```python import matplotlib.pyplot as plt # Heat added and corresponding temperatures q = [0, 20.9, 354.9, 772.9, 999.9, 1040.1] T = [-10, 0, 0, 100, 100, 120] # Create the plot plt.plot(q, T, marker='o') plt.xlabel('Heat Added (J)') plt.ylabel('Temperature (°C)') plt.title('Temperature vs Heat Added for Heating 1g Ice (-10°C to 120°C)') plt.grid(True) # Annotate segments plt.text(10, -5, 'Solid warms', fontsize=8) plt.text(200, 5, 'Melting', fontsize=8) plt.text(600, 50, 'Liquid warms', fontsize=8) plt.text(950, 105, 'Boiling', fontsize=8) plt.text(1030, 115, 'Gas warms', fontsize=8) plt.show() ``` ## Final Answer - The plot is a **stepwise graph**: temperature rises linearly with added heat during warming phases, with **constant (horizontal plateaus)** during phase changes (melting and boiling). - **Label the segments** as "Solid warms", "Melting", "Liquid warms", "Boiling", "Gas warms".  *Alt text: Stepwise plot of temperature versus heat added showing solid, melting, liquid, boiling, and gas phases.* > Note: Adjust parameters as necessary for your specific scenario or data.