The internal energy of a solid also increases when heat is transferred to it from its surroundings. A 5 kg solid bar is heated at atmospheric pressure. Its temperature increases from `20^@C` to `70^@C`. The linear expansion coefficient of solid bar is `1xx10^(-3)//^(@)C`. The density of solid bar is `50 kg//m^3`. The specific heat capacity of solid bar is `200 J//kgC^@`. The atmospheric pressure is `1xx10N//m^2`.
The heat transferred to the solid bar is

Options

A. 49000 J
B. 50000 J
C. 50500 J
D. 51000 J

Explanation

To find the heat transferred to the solid bar, we can use the formula for heat transfer, which is given by:

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

Where:
- \( Q \) = heat transferred (in Joules)
- \( m \) = mass of the solid bar (in kg)
- \( c \) = specific heat capacity of the solid bar (in J/kg°C)
- \( \Delta T \) = change in temperature (in °C)

### Step 1: Identify the given values
- Mass of the solid bar, \( m = 5 \, \text{kg} \)
- Initial temperature, \( T_i = 20 \, °C \)
- Final temperature, \( T_f = 70 \, °C \)
- Specific heat capacity, \( c = 200 \, \text{J/kg°C} \)

### Step 2: Calculate the change in temperature (\( \Delta T \))
\[ \Delta T = T_f - T_i = 70 \, °C - 20 \, °C = 50 \, °C \]

### Step 3: Substitute the values into the heat transfer formula
Now, we can substitute the values into the formula:
\[ Q = m \cdot c \cdot \Delta T \]
\[ Q = 5 \, \text{kg} \cdot 200 \, \text{J/kg°C} \cdot 50 \, °C \]

### Step 4: Perform the calculation
Calculating the product:
\[ Q = 5 \cdot 200 \cdot 50 \]
\[ Q = 1000 \cdot 50 = 50000 \, \text{J} \]

### Step 5: State the final answer
The heat transferred to the solid bar is:
\[ Q = 50000 \, \text{J} \]