Ranking Cycle Work Ratio Calculation

The Ranking cycle is a thermodynamic cycle that converts heat into work. It is the fundamental operating cycle for thermal power plants. The main components involved in a simple Ranking cycle are a boiler, turbine, condenser, and pump.

In a Ranking cycle, the turbine produces work from the expansion of steam, while the pump requires work to return the condensed water to the boiler pressure.

The net work output from the cycle is the difference between the work done by the turbine and the work consumed by the pump.

The work ratio is a parameter used to evaluate the performance of a cycle. It is defined as the ratio of the net work output to the gross work output (which is typically the turbine work in a Ranking cycle).

Mathematically, the work ratio ($r_w$) is given by:

$$ r_w = \frac{\text{Net Work Output}}{\text{Gross Work Output}} $$

In the context of the Ranking cycle:

$$ r_w = \frac{W_{net}}{W_T} = \frac{W_T - W_P}{W_T} $$

Where:

• $W_T$ is the work done by the turbine.
• $W_P$ is the work required by the pump.
• $W_{net}$ is the net work output ($W_T - W_P$).

From the question, we are given:

• Work done by the turbine, $W_T = 8 \text{ kJ}$
• Work required by the pump, $W_P = 6 \text{ kJ}$

Now, we can calculate the net work output:

$$ W_{net} = W_T - W_P $$

$$ W_{net} = 8 \text{ kJ} - 6 \text{ kJ} $$

$$ W_{net} = 2 \text{ kJ} $$

Next, we calculate the work ratio using the formula:

$$ r_w = \frac{W_{net}}{W_T} $$

$$ r_w = \frac{2 \text{ kJ}}{8 \text{ kJ}} $$

$$ r_w = 0.25 $$

Therefore, the work ratio for the given Ranking cycle is 0.25.