Heat energy of 10,000 J is supplied to a metal block of mass 600 g at atmospheric pressure. The initial temperature of the block is `20^@C`, specific heat of metal `= 300 J kg^(-1) C^(-1) ` , relative density of metal = 7.0, coefficient of volume expansion of metal `= 6 xx 10^(-5) ""^@C^(-1)` and atmospheric pressure, `P = 10^5` Pa. Also, Heat energy supplied = mass x specific heat x change in temperature
The final temperature of the block is

Options

A. `46.43^@C`
B. `55.55^@C`
C. `61.15^@C`
D. `75.55^@C`

Explanation

To find the final temperature of the metal block after supplying heat energy, we can use the formula for heat energy supplied:

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

Where:
- \( Q \) is the heat energy supplied (in joules),
- \( m \) is the mass of the metal block (in kg),
- \( c \) is the specific heat capacity (in J/kg°C),
- \( \Delta T \) is the change in temperature (in °C).

### Step 1: Convert mass from grams to kilograms
The mass of the metal block is given as 600 g. We need to convert this to kilograms:

\[ m = 600 \, \text{g} = \frac{600}{1000} \, \text{kg} = 0.6 \, \text{kg} \]

### Step 2: Identify the initial temperature
The initial temperature \( T_1 \) is given as:

\[ T_1 = 20 \, °C \]

### Step 3: Use the heat energy supplied
The heat energy supplied is given as:

\[ Q = 10,000 \, \text{J} \]

### Step 4: Use the specific heat capacity
The specific heat capacity \( c \) is given as:

\[ c = 300 \, \text{J/kg°C} \]

### Step 5: Rearrange the formula to find the change in temperature
We can rearrange the heat energy formula to solve for the change in temperature \( \Delta T \):

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

### Step 6: Substitute the known values into the equation
Substituting the known values into the equation gives:

\[ \Delta T = \frac{10,000 \, \text{J}}{0.6 \, \text{kg} \cdot 300 \, \text{J/kg°C}} = \frac{10,000}{180} \approx 55.56 \, °C \]

### Step 7: Calculate the final temperature
Now, we can find the final temperature \( T_2 \):

\[ T_2 = T_1 + \Delta T = 20 \, °C + 55.56 \, °C \approx 75.56 \, °C \]

### Final Answer
The final temperature of the block is approximately:

\[ \boxed{75.56 \, °C} \]