A Carnot engine working between K 300 and 600 K has work output of 800 J per cycle. What is amount of heat energy supplied to the engine from source per cycle

Options

A. 800 J
B. 1600 J
C. 3200 J
D. 6400J

Answer

To find the amount of heat energy supplied to the Carnot engine from the source per cycle, we can follow these steps:

### Step 1: Understand the Carnot Engine Efficiency Formula
The efficiency (η) of a Carnot engine is given by the formula:
\[ η = 1 - \frac{T_L}{T_H} \]
where \( T_L \) is the temperature of the cold reservoir (sink) and \( T_H \) is the temperature of the hot reservoir (source).

### Step 2: Identify the Given Values
From the problem, we have:
- \( T_H = 600 \, K \)
- \( T_L = 300 \, K \)
- Work output \( W = 800 \, J \)

### Step 3: Calculate the Efficiency
Substituting the values of \( T_L \) and \( T_H \) into the efficiency formula:
\[ η = 1 - \frac{300}{600} = 1 - 0.5 = 0.5 \]

### Step 4: Relate Efficiency to Work and Heat Input
The efficiency can also be expressed in terms of work output and heat input:
\[ η = \frac{W}{Q_H} \]
where \( Q_H \) is the heat energy supplied from the source.

### Step 5: Rearrange to Find \( Q_H \)
From the efficiency equation, we can rearrange it to solve for \( Q_H \):
\[ Q_H = \frac{W}{η} \]

### Step 6: Substitute the Known Values
Now we can substitute the known values into the equation:
\[ Q_H = \frac{800 \, J}{0.5} = 1600 \, J \]

### Conclusion
The amount of heat energy supplied to the engine from the source per cycle is:
\[ Q_H = 1600 \, J \]