A `5.0` amp current is setup in an external circuit by a `6.0` volt storage battery for `6.0` minutes. The chemical energy of the battery is reduced by

Options

A. `1.08xx10^4J`
B. `1.08xx10^(-4)J`
C. `1.8xx10^4J`
D. `1.8xx10^(-4)J`

Answer

To solve the problem of how much chemical energy is reduced in the battery, we can follow these steps:

### Step 1: Understand the relationship between power, current, and voltage
The power (P) produced in an electrical circuit can be calculated using the formula:
\[ P = V \times I \]
where:
- \( V \) is the voltage (in volts),
- \( I \) is the current (in amperes).

### Step 2: Substitute the given values
From the problem, we know:
- \( V = 6.0 \) volts,
- \( I = 5.0 \) amperes.

Now, we can calculate the power:
\[ P = 6.0 \, \text{V} \times 5.0 \, \text{A} = 30.0 \, \text{W} \]

### Step 3: Convert time from minutes to seconds
The time (t) for which the current flows is given as 6.0 minutes. We need to convert this into seconds:
\[ t = 6.0 \, \text{minutes} \times 60 \, \text{seconds/minute} = 360 \, \text{seconds} \]

### Step 4: Calculate the total energy (heat produced)
The total energy (E) produced can be calculated using the formula:
\[ E = P \times t \]
Substituting the values we have:
\[ E = 30.0 \, \text{W} \times 360 \, \text{s} = 10800 \, \text{J} \]

### Step 5: Convert the energy into scientific notation
To express the energy in scientific notation:
\[ E = 10800 \, \text{J} = 1.08 \times 10^4 \, \text{J} \]

### Conclusion
Thus, the chemical energy of the battery is reduced by \( 1.08 \times 10^4 \, \text{J} \).

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