A Carnot engine, having an efficiency of `eta=1//10` as heat engine, is used as a refrigerator. If the work done on the system is 10J, the amount of energy absorbed from the reservoir at lower temperature is

Options

A. `99J`
B. `90J`
C. `1J`
D. `100J`

Explanation

To solve the problem step by step, we will use the relationship between the efficiency of a Carnot engine and the coefficient of performance (COP) of a refrigerator.

### Step 1: Understand the relationship between efficiency and COP
The efficiency (η) of a Carnot engine is related to the coefficient of performance (β) of a refrigerator by the formula:
\[ \beta = \frac{1 - \eta}{\eta} \]

### Step 2: Substitute the given efficiency
Given that the efficiency of the Carnot engine is:
\[ \eta = \frac{1}{10} = 0.1 \]
We can substitute this value into the formula for β:
\[ \beta = \frac{1 - 0.1}{0.1} = \frac{0.9}{0.1} = 9 \]

### Step 3: Use the formula for COP
The coefficient of performance (β) for a refrigerator is also defined as:
\[ \beta = \frac{Q_2}{W} \]
where:
- \( Q_2 \) is the heat absorbed from the low-temperature reservoir,
- \( W \) is the work done on the system.

### Step 4: Substitute the known values
From the problem, we know that the work done \( W \) is 10 J. We can now substitute the values into the equation:
\[ 9 = \frac{Q_2}{10} \]

### Step 5: Solve for \( Q_2 \)
To find \( Q_2 \), we can rearrange the equation:
\[ Q_2 = 9 \times 10 = 90 \, \text{J} \]

### Conclusion
The amount of energy absorbed from the reservoir at lower temperature is:
\[ \boxed{90 \, \text{J}} \]

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