The amount of heat energy required to increase the temperature of 'X' g of water by `10 .^(@)C` is found to be 15 cal. Calculate 'X'.

Options

A. 0.5 g
B. 15 g
C. 1.5 g
D. 7.5 g

Explanation

To solve the problem, we need to use the formula for heat energy:

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

Where:
- \( Q \) is the heat energy (in calories),
- \( m \) is the mass of the water (in grams),
- \( c \) is the specific heat capacity of water (which is approximately \( 1 \, \text{cal/g}^\circ C \)),
- \( \Delta T \) is the change in temperature (in degrees Celsius).

Given:
- \( Q = 15 \, \text{cal} \)
- \( \Delta T = 10 \, \text{°C} \)
- \( c = 1 \, \text{cal/g}^\circ C \)

We need to find \( m \) (the mass of the water, which is represented as 'X').

### Step 1: Rearranging the formula
We can rearrange the formula to solve for \( m \):

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

### Step 2: Substituting the known values
Now, we can substitute the known values into the equation:

\[ m = \frac{15 \, \text{cal}}{1 \, \text{cal/g}^\circ C \cdot 10 \, \text{°C}} \]

### Step 3: Performing the calculation
Now, we perform the calculation:

\[ m = \frac{15 \, \text{cal}}{10 \, \text{cal/g}} \]

\[ m = 1.5 \, \text{g} \]

### Conclusion
Thus, the mass of water 'X' is:

\[ X = 1.5 \, \text{g} \]

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