Question

The compressor of a gas turbine plant, operating on an ideal intercooled Brayton cycle, accomplishes an overall pressure ratio of 6 in a two-stage compression process. Intercooling is used to cool the air coming out from the first stage to the inlet temperature of the first stage, before its entry to the second stage. Air enters the compressor at 300 K and 100 kPa. If the properties of gas are constant, the intercooling pressure for minimum compressor work is _______

• A. 321.15 kPa
• B. 479.16 kPa
• C. 244.95 kPa
• D. 195.35 kPa

Hint:

Whenever perfect intercooling is specified, the stage pressure ratios are equal:
$\frac{P_i}{P_1} = \frac{P_2}{P_i} \implies P_i = \sqrt{P_1 P_2}$. This is a classic result that is highly tested.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question asks for the optimal intermediate pressure (intercooling pressure) in a two-stage compression process with perfect intercooling to minimize total compressor work.

Step 2: Key Formula or Approach:
For minimum compressor work in a two-stage compression process with perfect intercooling, the intermediate pressure ($P_i$) is the geometric mean of the inlet pressure ($P_1$) and the outlet pressure ($P_2$):
\[ P_i = \sqrt{P_1 \cdot P_2} \]

Step 3: Detailed Explanation:

• Identify the given parameters:
- Inlet pressure, $P_1 = 100 \text{ kPa}$
- Overall pressure ratio, $r_p = \frac{P_2}{P_1} = 6$

• Calculate the final delivery pressure ($P_2$):
\[ P_2 = r_p \times P_1 = 6 \times 100 \text{ kPa} = 600 \text{ kPa} \]

• Apply the optimal intermediate pressure formula:
\[ P_i = \sqrt{P_1 \cdot P_2} = \sqrt{100 \times 600} \]
\[ P_i = \sqrt{60000} \]

• Calculate the square root:
\[ P_i \approx 244.9489 \text{ kPa} \approx 244.95 \text{ kPa} \]

Step 4: Final Answer:
The intercooling pressure for minimum compressor work is $244.95 \text{ kPa}$.