Calculate the energy required to heat 513.0 mg of mercury from 0 °C to 10.0 °C. Assume the specific heat capacity of mercury under these conditions is 0.139 J-g K Be sure your answer has the correct number of significant digits. ロロ の

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### Heat Energy Calculation

**Problem Statement:**
Calculate the energy required to heat 513.0 mg of mercury from 0°C to 10.0°C. Assume the specific heat capacity of mercury under these conditions is 0.139 J·g⁻¹·K⁻¹. Be sure your answer has the correct number of significant digits.

**Inputs and Explanation:**
- **Mass of mercury (m):** 513.0 mg (which needs to be converted to grams because the given specific heat capacity is in J·g⁻¹·K⁻¹)
- **Initial temperature (T₁):** 0°C
- **Final temperature (T₂):** 10.0°C
- **Specific heat capacity (c):** 0.139 J·g⁻¹·K⁻¹

**Conversion:**
1 mg = 0.001 g  
So, 513.0 mg = 513.0 * 0.001 g = 0.513 g

**Formula to use:**
The energy required (Q) can be calculated using the formula:
\[ Q = m \cdot c \cdot \Delta T \]
Where:
- \( Q \) is the heat energy (in joules, J)
- \( m \) is the mass (in grams, g)
- \( c \) is the specific heat capacity (J·g⁻¹·K⁻¹)
- \( \Delta T \) is the change in temperature (T₂ - T₁) (in Celsius or Kelvin, K since the difference in temperature in Celsius and Kelvin is the same)

**Calculation:**
1. Calculate the change in temperature (ΔT):
\[ \Delta T = T₂ - T₁ = 10.0°C - 0°C = 10.0 K \]

2. Substitute the values into the formula:
\[ Q = 0.513 \, \text{g} \times 0.139 \, \text{J·g}^{-1} \text{·K}^{-1} \times 10.0 \, \text{K} \]

\[ Q = 0.513 \times 0.139 \times 10.0 \]

\[ Q = 0.71307 \text{ J} \]

**Result:**
\[ Q = 0.713 \
Transcribed Image Text:### Heat Energy Calculation **Problem Statement:** Calculate the energy required to heat 513.0 mg of mercury from 0°C to 10.0°C. Assume the specific heat capacity of mercury under these conditions is 0.139 J·g⁻¹·K⁻¹. Be sure your answer has the correct number of significant digits. **Inputs and Explanation:** - **Mass of mercury (m):** 513.0 mg (which needs to be converted to grams because the given specific heat capacity is in J·g⁻¹·K⁻¹) - **Initial temperature (T₁):** 0°C - **Final temperature (T₂):** 10.0°C - **Specific heat capacity (c):** 0.139 J·g⁻¹·K⁻¹ **Conversion:** 1 mg = 0.001 g So, 513.0 mg = 513.0 * 0.001 g = 0.513 g **Formula to use:** The energy required (Q) can be calculated using the formula: \[ Q = m \cdot c \cdot \Delta T \] Where: - \( Q \) is the heat energy (in joules, J) - \( m \) is the mass (in grams, g) - \( c \) is the specific heat capacity (J·g⁻¹·K⁻¹) - \( \Delta T \) is the change in temperature (T₂ - T₁) (in Celsius or Kelvin, K since the difference in temperature in Celsius and Kelvin is the same) **Calculation:** 1. Calculate the change in temperature (ΔT): \[ \Delta T = T₂ - T₁ = 10.0°C - 0°C = 10.0 K \] 2. Substitute the values into the formula: \[ Q = 0.513 \, \text{g} \times 0.139 \, \text{J·g}^{-1} \text{·K}^{-1} \times 10.0 \, \text{K} \] \[ Q = 0.513 \times 0.139 \times 10.0 \] \[ Q = 0.71307 \text{ J} \] **Result:** \[ Q = 0.713 \
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