Gasoline has an enthalpy of combustion 24000 kJ/mol gallon. When gasoline burns in an automobile engine, approximately 30% of the energy released is used to produce mechanical work. The remainder is lost as heat transfer to the engine's cooling system. As a start on estimating how much heat transfer is required, calculate what mass of water could be heated from `25^(@)C` to `75^(@)C` by the combustion of 1.0 gallon of gasoline in an automobile? (Given : `C(H_(2)O)=4.18 J//g^(@)C`)

Options

A. 34.45 kg
B. 80.383 kg
C. 22 kg
D. 224 kg

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the energy available for heating water
Given that the enthalpy of combustion of gasoline is 24,000 kJ/gallon and only 30% of this energy is used for mechanical work, we need to find the energy that is lost as heat transfer.

The energy available for heating water (Q) can be calculated as:
\[ Q = 0.70 \times 24000 \, \text{kJ/gallon} \]
Calculating this gives:
\[ Q = 16800 \, \text{kJ/gallon} \]

### Step 2: Convert energy from kJ to J
Since the specific heat capacity of water is given in J/g°C, we need to convert kJ to J:
\[ Q = 16800 \, \text{kJ} \times 1000 \, \text{J/kJ} = 16800000 \, \text{J/gallon} \]

### Step 3: Determine the change in temperature (ΔT)
The change in temperature (ΔT) is given by:
\[ \Delta T = T_{final} - T_{initial} = 75°C - 25°C = 50°C \]

### Step 4: Use the formula \( Q = mc\Delta T \) to find the mass of water (m)
We can rearrange the formula to solve for mass (m):
\[ m = \frac{Q}{c \Delta T} \]
Where:
- \( Q = 16800000 \, \text{J} \)
- \( c = 4.18 \, \text{J/g°C} \)
- \( \Delta T = 50°C \)

Substituting the values into the equation:
\[ m = \frac{16800000 \, \text{J}}{4.18 \, \text{J/g°C} \times 50°C} \]

Calculating this gives:
\[ m = \frac{16800000}{209} \approx 80480.38 \, \text{g} \]

### Step 5: Convert grams to kilograms
To convert grams to kilograms, divide by 1000:
\[ m \approx 80.48 \, \text{kg} \]

### Final Answer
The mass of water that could be heated from 25°C to 75°C by the combustion of 1.0 gallon of gasoline in an automobile is approximately **80.48 kg**.

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