A electric kettle ( rated accurately at `2.5 kW`) is used to heat `3 kg` of water from `15^(@)C` to boiling point . It takes `9.5 min`. Then the amount of heat that has been lost is

Options

A. `3.5 xx 10^(5) J`
B. `7 xx 10^(8) J`
C. `3.5 xx 10^(4) J`
D. `7 xx 10^(8) J`

Explanation

To solve the problem step by step, we will calculate the heat consumed by the kettle, the heat used to raise the temperature of the water, and finally the heat lost.

### Step 1: Calculate the Heat Consumed by the Kettle
The power of the kettle is given as \( P = 2.5 \, \text{kW} = 2.5 \times 10^3 \, \text{W} \). The time taken to heat the water is \( t = 9.5 \, \text{min} = 9.5 \times 60 \, \text{s} = 570 \, \text{s} \).

The heat consumed by the kettle can be calculated using the formula:
\[ Q_{\text{consumed}} = P \times t \]
Substituting the values:
\[ Q_{\text{consumed}} = 2.5 \times 10^3 \, \text{W} \times 570 \, \text{s} = 1,425,000 \, \text{J} = 14.25 \times 10^5 \, \text{J} \]

### Step 2: Calculate the Heat Used to Raise the Temperature of Water
The mass of water is given as \( m = 3 \, \text{kg} \). The specific heat capacity of water is \( s = 4.2 \times 10^3 \, \text{J/kg°C} \). The initial temperature is \( T_i = 15 \, °C \) and the final temperature (boiling point) is \( T_f = 100 \, °C \).

The change in temperature \( \Delta T \) is:
\[ \Delta T = T_f - T_i = 100 - 15 = 85 \, °C \]

The heat used to raise the temperature of the water can be calculated using the formula:
\[ Q_{\text{used}} = m \times s \times \Delta T \]
Substituting the values:
\[ Q_{\text{used}} = 3 \, \text{kg} \times 4.2 \times 10^3 \, \text{J/kg°C} \times 85 \, °C \]
Calculating this gives:
\[ Q_{\text{used}} = 3 \times 4.2 \times 85 \times 10^3 = 1,071,000 \, \text{J} = 10.71 \times 10^5 \, \text{J} \]

### Step 3: Calculate the Heat Lost
The heat lost by the kettle can be calculated as:
\[ Q_{\text{lost}} = Q_{\text{consumed}} - Q_{\text{used}} \]
Substituting the values:
\[ Q_{\text{lost}} = 14.25 \times 10^5 \, \text{J} - 10.71 \times 10^5 \, \text{J} = 3.54 \times 10^5 \, \text{J} \]

### Final Answer
The amount of heat that has been lost is:
\[ Q_{\text{lost}} = 3.54 \times 10^5 \, \text{J} \]