An electrically heated coil is immersed in a calorimeter containing 360 g of water at `10^@C`. The coil consumes energy at the rate of 90 W. The water equivalent of calorimeter and coil is 40 g. The temperature of water after 10 min is

Options

A. `4.214^@C`
B. `42.14^@C`
C. `30^@C`
D. none of these

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the total energy supplied by the coil.
The power of the coil is given as 90 W, and it operates for 10 minutes. First, we need to convert the time into seconds.

\[ \text{Time in seconds} = 10 \text{ minutes} \times 60 \text{ seconds/minute} = 600 \text{ seconds} \]

Now, we can calculate the energy supplied by the coil using the formula:

\[ \text{Energy (Q)} = \text{Power} \times \text{Time} \]

Substituting the values:

\[ Q = 90 \text{ W} \times 600 \text{ s} = 54000 \text{ J} \]

### Step 2: Determine the effective mass of the system.
The mass of the water is given as 360 g, and the water equivalent of the calorimeter and coil is 40 g. The total effective mass (m) that will absorb the heat is:

\[ m = \text{mass of water} + \text{water equivalent of calorimeter} = 360 \text{ g} + 40 \text{ g} = 400 \text{ g} \]

### Step 3: Use the specific heat capacity to find the temperature change.
The specific heat capacity of water (c) is approximately \(4.2 \, \text{J/g°C}\). We can use the formula:

\[ Q = m \cdot c \cdot \Delta T \]

Where \(\Delta T\) is the change in temperature. Rearranging the formula to find \(\Delta T\):

\[ \Delta T = \frac{Q}{m \cdot c} \]

Substituting the known values:

\[ \Delta T = \frac{54000 \text{ J}}{400 \text{ g} \times 4.2 \text{ J/g°C}} = \frac{54000}{1680} \approx 32.14 \text{ °C} \]

### Step 4: Calculate the final temperature.
The initial temperature of the water is \(10 \text{ °C}\). Therefore, the final temperature (\(T_f\)) is:

\[ T_f = T_i + \Delta T = 10 \text{ °C} + 32.14 \text{ °C} \approx 42.14 \text{ °C} \]

### Final Answer:
The final temperature of the water after 10 minutes is approximately \(42.14 \text{ °C}\).

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