Temperature of 100 gm water is changed from `0^@C " to " 3^@C` . In this process , heat supplied to water will be (specified heat of water `1 cal g^(-1) .^@C^(-1))`

Options

A. Equal to 300 cal
B. Greater than 300 cal
C. Less than 300 cal
D. Data is insufficient

Answer

To solve the problem, we need to calculate the heat supplied to 100 grams of water when its temperature changes from \(0^\circ C\) to \(3^\circ C\). The specific heat of water is given as \(1 \, \text{cal/g} \cdot {}^\circ C\).

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass of water, \(m = 100 \, \text{g}\)
- Initial temperature, \(T_i = 0^\circ C\)
- Final temperature, \(T_f = 3^\circ C\)
- Specific heat of water, \(s = 1 \, \text{cal/g} \cdot {}^\circ C\)

2. **Calculate the change in temperature (\(\Delta T\)):**
\[ \Delta T = T_f - T_i = 3^\circ C - 0^\circ C = 3^\circ C \]

3. **Use the formula for heat supplied (\(Q\)):**
The formula for calculating heat supplied is:
\[ Q = m \cdot s \cdot \Delta T \]
Substituting the values we have:
\[ Q = 100 \, \text{g} \cdot 1 \, \text{cal/g} \cdot {}^\circ C \cdot 3^\circ C \]

4. **Calculate \(Q\):**
\[ Q = 100 \cdot 1 \cdot 3 = 300 \, \text{cal} \]

5. **Consider the temperature dependency of specific heat:**
The specific heat of water is temperature dependent. The given specific heat value of \(1 \, \text{cal/g} \cdot {}^\circ C\) is valid for a specific temperature range (around \(14.5^\circ C\) to \(15.5^\circ C\)). Since the temperature change from \(0^\circ C\) to \(3^\circ C\) is below this range, the actual specific heat may be less than \(1 \, \text{cal/g} \cdot {}^\circ C\).

6. **Conclusion:**
Therefore, the heat supplied to the water will be less than \(300 \, \text{cal}\).

### Final Answer:
The heat supplied to the water will be less than \(300 \, \text{cal}\).

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