A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 7.10 kg of water at 30.0 °c. During the reaction 150. kJ of heat flows out of the bath and into the flask. Calculate the new temperature of the water bath. You can assume the specific heat capacity of water under these conditions is 4.18 J-g'K'. Round your answer to 3 significant digits. do
A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 7.10 kg of water at 30.0 °c. During the reaction 150. kJ of heat flows out of the bath and into the flask. Calculate the new temperature of the water bath. You can assume the specific heat capacity of water under these conditions is 4.18 J-g'K'. Round your answer to 3 significant digits. do
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![**Thermodynamics Example: Calculating the New Temperature of a Water Bath**
**Problem Statement:**
A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains \( 7.10 \, \text{kg} \) of water at \( 30.0 \, ^\circ\text{C} \). During the reaction, \( 150. \, \text{kJ} \) of heat flows out of the bath and into the flask.
**Task:**
Calculate the new temperature of the water bath. You can assume the specific heat capacity of water under these conditions is \( 4.18 \, \text{J} \cdot \text{g}^{-1} \cdot \text{K}^{-1} \). Round your answer to 3 significant digits.
**Solution Steps:**
To determine the new temperature of the water bath, we'll use the formula:
\[ q = mc\Delta T \]
Where:
- \( q \) is the heat energy transferred (in joules, \( J \))
- \( m \) is the mass of the water (in kilograms, converted to grams for this calculation)
- \( c \) is the specific heat capacity of water (in \( \text{J} \cdot \text{g}^{-1} \cdot \text{K}^{-1} \))
- \( \Delta T \) is the change in temperature (in \( ^\circ\text{C} \) or \( K \))
1. Convert the mass of water into grams:
\[ 7.10 \, \text{kg} \times 1000 \, \frac{\text{g}}{\text{kg}} = 7100 \, \text{g} \]
2. Convert the heat energy from kilojoules to joules:
\[ 150. \, \text{kJ} \times 1000 \, \frac{J}{\text{kJ}} = 150 \, 000 \, \text{J} \]
3. Rearrange the formula and solve for \( \Delta T \):
\[ \Delta T = \frac{q}{mc} = \frac{150 \, 000 \, \text{J}}{7100 \, \text{g} \times 4.18 \, \text{J} \cd](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9e44953-88de-40ab-8a7d-f595eabb1d43%2F5b0936f2-280e-40c6-b7d4-e8f768ebcd61%2Fhlx04qk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Thermodynamics Example: Calculating the New Temperature of a Water Bath**
**Problem Statement:**
A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains \( 7.10 \, \text{kg} \) of water at \( 30.0 \, ^\circ\text{C} \). During the reaction, \( 150. \, \text{kJ} \) of heat flows out of the bath and into the flask.
**Task:**
Calculate the new temperature of the water bath. You can assume the specific heat capacity of water under these conditions is \( 4.18 \, \text{J} \cdot \text{g}^{-1} \cdot \text{K}^{-1} \). Round your answer to 3 significant digits.
**Solution Steps:**
To determine the new temperature of the water bath, we'll use the formula:
\[ q = mc\Delta T \]
Where:
- \( q \) is the heat energy transferred (in joules, \( J \))
- \( m \) is the mass of the water (in kilograms, converted to grams for this calculation)
- \( c \) is the specific heat capacity of water (in \( \text{J} \cdot \text{g}^{-1} \cdot \text{K}^{-1} \))
- \( \Delta T \) is the change in temperature (in \( ^\circ\text{C} \) or \( K \))
1. Convert the mass of water into grams:
\[ 7.10 \, \text{kg} \times 1000 \, \frac{\text{g}}{\text{kg}} = 7100 \, \text{g} \]
2. Convert the heat energy from kilojoules to joules:
\[ 150. \, \text{kJ} \times 1000 \, \frac{J}{\text{kJ}} = 150 \, 000 \, \text{J} \]
3. Rearrange the formula and solve for \( \Delta T \):
\[ \Delta T = \frac{q}{mc} = \frac{150 \, 000 \, \text{J}}{7100 \, \text{g} \times 4.18 \, \text{J} \cd
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