A 10 kg storage battery has an average specific heat of `0.2 "kcal/kg".^@C`. When fully charged, the energy content of the battery is 1 kcal. If the entire energy were used to raise the temperature, then the temperature would increase by

Options

A. `0.2^@C`
B. `0.5^@C`
C. `200^@C`
D. `20^@C`

Answer

To solve the problem, we need to find out how much the temperature of the battery will increase when the entire energy content of the battery is used to raise its temperature. We can use the formula related to specific heat to find this.

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass of the battery (m) = 10 kg
- Specific heat (c) = 0.2 kcal/kg°C
- Energy content (Q) = 1 kcal

2. **Use the formula for heat transfer:**
The formula to calculate the change in temperature (ΔT) when a certain amount of heat (Q) is added to a substance is given by:
\[ Q = mc\Delta T \]
Where:
- Q = heat energy (in kcal)
- m = mass (in kg)
- c = specific heat (in kcal/kg°C)
- ΔT = change in temperature (in °C)

3. **Rearranging the formula to find ΔT:**
We can rearrange the formula to solve for ΔT:
\[ \Delta T = \frac{Q}{mc} \]

4. **Substituting the values into the formula:**
Now, substitute the known values into the equation:
\[ \Delta T = \frac{1 \text{ kcal}}{10 \text{ kg} \times 0.2 \text{ kcal/kg°C}} \]

5. **Calculating ΔT:**
- First, calculate the denominator:
\[ 10 \text{ kg} \times 0.2 \text{ kcal/kg°C} = 2 \text{ kcal/°C} \]
- Now, substitute this back into the equation:
\[ \Delta T = \frac{1 \text{ kcal}}{2 \text{ kcal/°C}} = 0.5 °C \]

6. **Conclusion:**
The temperature of the battery would increase by **0.5 °C**.

### Final Answer:
The temperature would increase by **0.5 °C**.

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