If a steam engine delivers `6.0xx10^(8)J` of work per minute and absorbs `5.4xx10^(9)J` of heat per minute from its boiler then the efficiency of the engine is

Options

A. 0.11
B. 0.12
C. 0.13
D. 0.14

Explanation

To find the efficiency of the steam engine, we can use the formula for efficiency (η), which is defined as the ratio of work output (W) to heat input (Q):

\[ \eta = \frac{W}{Q} \]

### Step 1: Identify the given values
- Work output (W) = \(6.0 \times 10^8 \, \text{J}\) per minute
- Heat input (Q) = \(5.4 \times 10^9 \, \text{J}\) per minute

### Step 2: Substitute the values into the efficiency formula
Now we will substitute the values of W and Q into the efficiency formula:

\[ \eta = \frac{6.0 \times 10^8 \, \text{J}}{5.4 \times 10^9 \, \text{J}} \]

### Step 3: Simplify the fraction
To simplify the fraction, we can divide both the numerator and the denominator by \(10^8\):

\[ \eta = \frac{6.0}{5.4 \times 10^1} = \frac{6.0}{54} \]

### Step 4: Calculate the efficiency
Now we perform the division:

\[ \eta = \frac{6.0}{54} = 0.1111 \ldots \]

### Step 5: Express the efficiency as a decimal
Thus, we can express the efficiency as:

\[ \eta \approx 0.11 \]

### Conclusion
The efficiency of the steam engine is approximately \(0.11\) or \(11\%\).

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