A continuous flow water heater (geyser) has an electrical power rating = 2 k W and efficiently of conversion of electrical power into heat = 80%. If water is flowing through the device at the rate of 100 cc/sec, and the inlet temperature is 10 °C, the outlet temperature will be

Options

A. `12.2^@ C`
B. `13.8^@ C`
C. `20^@ C`
D. `16.5^@ C`

Answer

To find the outlet temperature of the water flowing through the continuous flow water heater (geyser), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Electrical power rating of the geyser, \( P = 2 \, \text{kW} = 2000 \, \text{W} \)
- Efficiency of conversion to heat, \( \eta = 80\% = 0.8 \)
- Flow rate of water, \( Q = 100 \, \text{cc/sec} = 100 \, \text{g/sec} \) (since the density of water is \( 1 \, \text{g/cm}^3 \))
- Inlet temperature of water, \( T_{in} = 10 \, \text{°C} \)

2. **Calculate the effective power converted to heat:**
\[ P_{heat} = \eta \times P = 0.8 \times 2000 \, \text{W} = 1600 \, \text{W} \]

3. **Calculate the heat energy supplied to the water per second:**
Since \( 1 \, \text{W} = 1 \, \text{J/s} \), the heat energy supplied per second is:
\[ Q_{heat} = 1600 \, \text{J/s} \]

4. **Use the formula for heat transfer:**
The heat energy supplied to the water can be expressed using the formula:
\[ Q_{heat} = m \cdot c \cdot \Delta T \]
where:
- \( m = 100 \, \text{g} = 0.1 \, \text{kg} \) (mass of water flowing per second)
- \( c = 4187 \, \text{J/(kg·K)} \) (specific heat capacity of water)
- \( \Delta T = T_{out} - T_{in} \) (change in temperature)

5. **Rearranging the equation to find \( \Delta T \):**
\[ \Delta T = \frac{Q_{heat}}{m \cdot c} = \frac{1600 \, \text{J}}{0.1 \, \text{kg} \cdot 4187 \, \text{J/(kg·K)}} \]

6. **Calculating \( \Delta T \):**
\[ \Delta T = \frac{1600}{0.1 \times 4187} = \frac{1600}{418.7} \approx 3.82 \, \text{K} \]

7. **Calculate the outlet temperature:**
\[ T_{out} = T_{in} + \Delta T = 10 \, \text{°C} + 3.82 \, \text{K} \approx 13.82 \, \text{°C} \]

### Final Answer:
The outlet temperature of the water will be approximately **13.82 °C**.