Question
The total amount of energy released when 45 g of 175 ° C' steam is cooled to 90°C is _ Reminder: As steam is condensed it will turn into water at 100 ° C. Round your answer to the nearest whole number. (1 point)
A. 417,600 J
B. 317,781 J
C.110,432 J
D.101,700 J
A. 417,600 J
B. 317,781 J
C.110,432 J
D.101,700 J
Answers
GPT-4o mini
To calculate the total energy released when 45 g of steam at 175 °C is cooled to 90 °C, we need to consider the following steps:
1. **Cooling the steam from 175 °C to 100 °C** (steam)
2. **Condensing the steam to water at 100 °C**
3. **Cooling the water from 100 °C to 90 °C**
### Step 1: Cooling steam from 175 °C to 100 °C
The specific heat capacity of steam is approximately \( 2.09 \, \text{J/g°C} \).
The energy (q) released when cooling the steam can be calculated using the formula:
\[
q = m \cdot c \cdot \Delta T
\]
Where:
- \( m = 45 \, \text{g} \)
- \( c = 2.09 \, \text{J/g°C} \)
- \( \Delta T = (100 - 175) = -75 \, \text{°C} \)
\[
q = 45 \, \text{g} \cdot 2.09 \, \text{J/g°C} \cdot (-75 \, \text{°C})
\]
\[
q = 45 \cdot 2.09 \cdot (-75) = -7016.25 \, \text{J}
\]
### Step 2: Condensing the steam to water at 100 °C
The heat of vaporization of water is \( 2260 \, \text{J/g} \).
The energy released during condensation is calculated as follows:
\[
q = m \cdot L
\]
Where:
- \( L = 2260 \, \text{J/g} \)
\[
q = 45 \, \text{g} \cdot 2260 \, \text{J/g}
\]
\[
q = 101700 \, \text{J}
\]
### Step 3: Cooling the water from 100 °C to 90 °C
The specific heat capacity of water is approximately \( 4.18 \, \text{J/g°C} \).
The energy released when cooling the water can also be calculated using the formula:
\[
q = m \cdot c \cdot \Delta T
\]
Where:
- \( \Delta T = (90 - 100) = -10 \, \text{°C} \)
\[
q = 45 \, \text{g} \cdot 4.18 \, \text{J/g°C} \cdot (-10 \, \text{°C})
\]
\[
q = 45 \cdot 4.18 \cdot (-10) = -1881 \, \text{J}
\]
### Total energy released
Now, we will sum the energies from all three steps:
1. Cooling steam: \( -7016.25 \, \text{J} \)
2. Condensing steam: \( -101700 \, \text{J} \)
3. Cooling water: \( -1881 \, \text{J} \)
Total:
\[
q_{\text{total}} = -7016.25 - 101700 - 1881 = -110597.25 \, \text{J}
\]
The total amount of energy released (ignoring the negative sign) is approximately:
\[
110597.25 \, \text{J} \approx 110,432 \, \text{J} \; (\text{rounded to the nearest whole number})
\]
Thus, the correct answer is **C. 110,432 J**.
1. **Cooling the steam from 175 °C to 100 °C** (steam)
2. **Condensing the steam to water at 100 °C**
3. **Cooling the water from 100 °C to 90 °C**
### Step 1: Cooling steam from 175 °C to 100 °C
The specific heat capacity of steam is approximately \( 2.09 \, \text{J/g°C} \).
The energy (q) released when cooling the steam can be calculated using the formula:
\[
q = m \cdot c \cdot \Delta T
\]
Where:
- \( m = 45 \, \text{g} \)
- \( c = 2.09 \, \text{J/g°C} \)
- \( \Delta T = (100 - 175) = -75 \, \text{°C} \)
\[
q = 45 \, \text{g} \cdot 2.09 \, \text{J/g°C} \cdot (-75 \, \text{°C})
\]
\[
q = 45 \cdot 2.09 \cdot (-75) = -7016.25 \, \text{J}
\]
### Step 2: Condensing the steam to water at 100 °C
The heat of vaporization of water is \( 2260 \, \text{J/g} \).
The energy released during condensation is calculated as follows:
\[
q = m \cdot L
\]
Where:
- \( L = 2260 \, \text{J/g} \)
\[
q = 45 \, \text{g} \cdot 2260 \, \text{J/g}
\]
\[
q = 101700 \, \text{J}
\]
### Step 3: Cooling the water from 100 °C to 90 °C
The specific heat capacity of water is approximately \( 4.18 \, \text{J/g°C} \).
The energy released when cooling the water can also be calculated using the formula:
\[
q = m \cdot c \cdot \Delta T
\]
Where:
- \( \Delta T = (90 - 100) = -10 \, \text{°C} \)
\[
q = 45 \, \text{g} \cdot 4.18 \, \text{J/g°C} \cdot (-10 \, \text{°C})
\]
\[
q = 45 \cdot 4.18 \cdot (-10) = -1881 \, \text{J}
\]
### Total energy released
Now, we will sum the energies from all three steps:
1. Cooling steam: \( -7016.25 \, \text{J} \)
2. Condensing steam: \( -101700 \, \text{J} \)
3. Cooling water: \( -1881 \, \text{J} \)
Total:
\[
q_{\text{total}} = -7016.25 - 101700 - 1881 = -110597.25 \, \text{J}
\]
The total amount of energy released (ignoring the negative sign) is approximately:
\[
110597.25 \, \text{J} \approx 110,432 \, \text{J} \; (\text{rounded to the nearest whole number})
\]
Thus, the correct answer is **C. 110,432 J**.