Calculate the time required to heat `20kg` of water from `10^(@)C to 35^(@)C ` using an immersion heater `1000W` Assume that `80%` of the power input is used to heat the water. Specific heat capacity of water `= 4200J kg^(-1)K^(-1)`

Explanation

To calculate the time required to heat 20 kg of water from 10°C to 35°C using a 1000W immersion heater, we can follow these steps:

### Step 1: Calculate the heat required to raise the temperature of the water.
The formula to calculate the heat required (Q) is given by:
\[ Q = m \cdot c \cdot \Delta T \]
where:
- \( m \) = mass of water = 20 kg
- \( c \) = specific heat capacity of water = 4200 J/(kg·K)
- \( \Delta T \) = change in temperature = final temperature - initial temperature = \( 35°C - 10°C = 25°C \)

Substituting the values:
\[ Q = 20 \, \text{kg} \cdot 4200 \, \text{J/(kg·K)} \cdot 25 \, \text{K} \]

Calculating this:
\[ Q = 20 \cdot 4200 \cdot 25 = 21 \times 10^5 \, \text{J} \]

### Step 2: Determine the effective power of the heater.
Since only 80% of the power input is used to heat the water, we need to calculate the effective power (P_eff):
\[ P_{\text{eff}} = P \cdot \text{Efficiency} \]
where:
- \( P \) = power of the heater = 1000 W
- Efficiency = 80% = 0.8

Substituting the values:
\[ P_{\text{eff}} = 1000 \, \text{W} \cdot 0.8 = 800 \, \text{W} \]

### Step 3: Relate the heat required to the power and time.
The energy provided by the heater over time (T) is given by:
\[ Q = P_{\text{eff}} \cdot T \]
Rearranging this gives:
\[ T = \frac{Q}{P_{\text{eff}}} \]

Substituting the values:
\[ T = \frac{21 \times 10^5 \, \text{J}}{800 \, \text{W}} \]

Calculating this:
\[ T = \frac{21 \times 10^5}{800} = 2625 \, \text{s} \]

### Step 4: Convert time from seconds to minutes.
To convert seconds to minutes, we divide by 60:
\[ T_{\text{minutes}} = \frac{2625 \, \text{s}}{60} \approx 43.75 \, \text{minutes} \]

Rounding this gives approximately:
\[ T \approx 44 \, \text{minutes} \]

### Final Answer:
The time required to heat 20 kg of water from 10°C to 35°C using a 1000W immersion heater is approximately **44 minutes**.

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