Question

For an ideal Rankine cycle operating between pressure of 30 bar and 0.04 bar the work output from the turbine is 903kJ/kg and the work input to the feed pump is 3kJ/kg. The specific steam consumption is ________ kg/kWh

• A. 2
• B. 4
• C. 6
• D. 8

Hint:

Remember the standard factor of 3600 in the numerator for calculating specific steam consumption.
If net work is in $\text{kJ/kg}$, dividing 3600 by the net work gives the steam consumption in $\text{kg/kWh}$ directly.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the specific steam consumption (SSC) of an ideal Rankine cycle.
The specific steam consumption represents the mass flow rate of steam required to produce a unit of net electrical or mechanical power output.
It is a key performance index used to estimate the size and capacity of the steam generator and auxiliary equipment.

Step 2: Key Formula or Approach:
The net work output (\(W_{\text{net}}\)) of the Rankine cycle is calculated as:
\[ W_{\text{net}} = W_{\text{turbine}} - W_{\text{pump}} \]
The specific steam consumption (SSC) in \(\text{kg/kWh}\) is calculated using the relation:
\[ \text{SSC} = \frac{3600}{W_{\text{net}}} \]
where \(W_{\text{net}}\) is expressed in \(\text{kJ/kg}\).

Step 3: Detailed Explanation:

• Identify the given parameters from the problem:
Turbine work output, \(W_{\text{turbine}} = 903\text{ kJ/kg}\).
Pump work input, \(W_{\text{pump}} = 3\text{ kJ/kg}\).

• Compute the net work output of the cycle:
\[ W_{\text{net}} = 903 - 3 = 900\text{ kJ/kg} \]

• Calculate the specific steam consumption using the standard conversion factor (\(1\text{ kWh} = 3600\text{ kJ}\)):
\[ \text{SSC} = \frac{3600\text{ kJ/kWh}}{900\text{ kJ/kg}} = 4\text{ kg/kWh} \]

Step 4: Final Answer:
The specific steam consumption of the Rankine cycle is \(4\text{ kg/kWh}\).