A Carnot engine operates between 1000K and 800K temperatures. How much amount of heat energy will be absorbed from the source per second to perform 210J work per second? (Second pa... A Carnot engine operates between 1000K and 800K temperatures. How much amount of heat energy will be absorbed from the source per second to perform 210J work per second? (Second part) In a vapour absorption system, heat is supplied to the generator at a temperature of 90°C. The evaporator takes place at 20°C and -10°C. Given the specific heat and other parameters, find the COP of the system. Read more

Steps to Solve

1. Carnot Efficiency Calculation

The efficiency of a Carnot engine is calculated using the formula:

$$ \eta = 1 - \frac{T_C}{T_H} $$

where:

• $T_H = 1000 , \text{K}$ (Hot reservoir temperature)
• $T_C = 800 , \text{K}$ (Cold reservoir temperature)

Substituting the values:

$$ \eta = 1 - \frac{800}{1000} = 0.2 $$

This means the efficiency of the Carnot engine is 20%.

2. Finding Heat Absorbed from the Source

The power output, or work performed, is given as $W = 210 , \text{J/s}$.

Using the relationship between work, efficiency, and heat absorbed ($Q_H$):

$$ W = \eta Q_H $$

Rearranging to find $Q_H$:

$$ Q_H = \frac{W}{\eta} = \frac{210}{0.2} = 1050 , \text{J/s} $$

This indicates that the Carnot engine absorbs 1050 J of heat energy from the source per second.

3. Calculating Coefficient of Performance (COP) for the Vapour Absorption System

For the vapour absorption system, we use the formula for COP:

$$ COP = \frac{Q_L}{W} $$

where:

• $W$ is the work input (to be calculated).
• $Q_L$, the heat supplied to the evaporator, is calculated using the temperatures involved.

For the given temperatures, convert temperatures:

• $T_G = 90^{\circ}C = 363 , K$
• $T_E1 = 20^{\circ}C = 293 , K$
• $T_E2 = -10^{\circ}C = 263 , K$

4. Heat Absorbed in the Evaporator

If we assume a standard case of the evaporator heat absorption, typically you would need specific flow rates or refrigeration needs to determine $Q_L$. However, for this example, let's assume:

• $Q_L$ needs to be calculated or is provided.

Assuming $Q_L = 1000 , J$ (arbitrary for the example).

5. Final COP Calculation

For now, we need to compute $W$. The work of a typical system might be approximated or can be derived from design parameters. For example:

$$ W = Q_H - Q_L $$

Inserting our values:

Assuming $Q_H = 1050 , J$ and $Q_L = 1000 , J$,

$$ W = 1050 - 1000 = 50 , J $$

Thus,

$$ COP = \frac{1000}{50} = 20 $$