If `0.5"cal" g^(-1) C^(-1)` is the specific heat capacity of a substance of mass 50 g, calculate the amount of heat energy required to change the temperature of a substance from `-5^(@)C` to `10^(@)C`

Options

A. 250 cal
B. 125 cal
C. 375 cal
D. 500 cal

Answer

To calculate the amount of heat energy required to change the temperature of a substance, we can use the formula:

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

Where:
- \( Q \) = amount of heat energy (in calories)
- \( m \) = mass of the substance (in grams)
- \( s \) = specific heat capacity (in calories per gram per degree Celsius)
- \( \Delta T \) = change in temperature (in degrees Celsius)

### Step 1: Identify the given values
- Specific heat capacity, \( s = 0.5 \, \text{cal} \, \text{g}^{-1} \, \text{C}^{-1} \)
- Mass of the substance, \( m = 50 \, \text{g} \)
- Initial temperature, \( T_i = -5 \, \text{C} \)
- Final temperature, \( T_f = 10 \, \text{C} \)

### Step 2: Calculate the change in temperature (\( \Delta T \))
\[ \Delta T = T_f - T_i \]
\[ \Delta T = 10 \, \text{C} - (-5 \, \text{C}) \]
\[ \Delta T = 10 \, \text{C} + 5 \, \text{C} \]
\[ \Delta T = 15 \, \text{C} \]

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the formula:
\[ Q = m \cdot s \cdot \Delta T \]
\[ Q = 50 \, \text{g} \cdot 0.5 \, \text{cal} \, \text{g}^{-1} \, \text{C}^{-1} \cdot 15 \, \text{C} \]

### Step 4: Perform the calculation
\[ Q = 50 \cdot 0.5 \cdot 15 \]
\[ Q = 25 \cdot 15 \]
\[ Q = 375 \, \text{cal} \]

### Final Answer
The amount of heat energy required is \( Q = 375 \, \text{cal} \).

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