Given that the ratio of specific heat capacity of alcohol to that of water is 13 : 25, which of the following statements is true?
A: When temperature is raised through `1^(@)C` the heat energy absorbed by 2 kg of alcohol is less than the heat energy absorbed by 1 kg of water.
B: Heat capacity of 2 kg alcohol is more than the heat capacity of 1 kg water.

Options

A. A is true and B is false.
B. A and B are true.
C. A is false and B is true.
D. A and B are false.

Answer

To solve the problem, we need to analyze the two statements given the ratio of specific heat capacities of alcohol and water, which is 13:25.

### Step 1: Understand the Specific Heat Capacity
The specific heat capacity (C) is defined as the amount of heat required to raise the temperature of 1 kg of a substance by 1°C.

### Step 2: Define the Variables
Let:
- \( C_a \) = specific heat capacity of alcohol
- \( C_w \) = specific heat capacity of water

From the problem, we know:
- \( C_a : C_w = 13 : 25 \)

This means we can express:
- \( C_a = 13k \)
- \( C_w = 25k \)
for some constant \( k \).

### Step 3: Calculate Heat Absorbed by Alcohol and Water
Using the formula for heat absorbed:
\[ Q = m \cdot C \cdot \Delta T \]
where:
- \( m \) = mass
- \( C \) = specific heat capacity
- \( \Delta T \) = change in temperature

#### For Alcohol:
- Mass \( m_a = 2 \) kg
- Specific heat capacity \( C_a = 13k \)
- Temperature change \( \Delta T = 1°C \)

So, the heat absorbed by alcohol \( Q_a \) is:
\[ Q_a = 2 \cdot (13k) \cdot 1 = 26k \]

#### For Water:
- Mass \( m_w = 1 \) kg
- Specific heat capacity \( C_w = 25k \)
- Temperature change \( \Delta T = 1°C \)

So, the heat absorbed by water \( Q_w \) is:
\[ Q_w = 1 \cdot (25k) \cdot 1 = 25k \]

### Step 4: Compare the Heat Absorbed
Now we compare \( Q_a \) and \( Q_w \):
- \( Q_a = 26k \)
- \( Q_w = 25k \)

Since \( 26k > 25k \), the heat absorbed by 2 kg of alcohol is greater than that absorbed by 1 kg of water.

### Step 5: Evaluate Statement A
Statement A claims that the heat energy absorbed by 2 kg of alcohol is less than that absorbed by 1 kg of water. Since we found that \( Q_a > Q_w \), Statement A is **false**.

### Step 6: Evaluate Statement B
Now, we calculate the heat capacities:
- Heat capacity of alcohol \( C_a = m_a \cdot C_a = 2 \cdot (13k) = 26k \)
- Heat capacity of water \( C_w = m_w \cdot C_w = 1 \cdot (25k) = 25k \)

Since \( 26k > 25k \), the heat capacity of 2 kg of alcohol is greater than that of 1 kg of water. Therefore, Statement B is **true**.

### Conclusion
- Statement A is false.
- Statement B is true.

Thus, the correct answer is that Statement B is true.

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