He compressor of a gas turbine plant, operating on an ideal intercooled Brayton cycle, accomplishes an overall compression 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________ kPa (round off to 2 decimal places).

The correct answer is 244.94 (or 244.95 using direct calculations).

To find the optimal intercooling pressure for a two-stage compressor that minimizes the work input, we analyze the thermodynamics of the multi-stage compression process with perfect intercooling.

For a two-stage compression process where the air is intercooled back to the initial inlet temperature, the minimum compressor work is achieved when the pressure ratio across each stage is equal. Let:
- $P_1$ be the inlet pressure to the first stage compressor.
- $P_i$ be the intermediate (intercooling) pressure.
- $P_2$ be the final delivery pressure after the second stage compressor.

The overall pressure ratio is given as:
$r_p=6$

The inlet pressure to the first stage is:
$P_1=100\text{kPa}$

Since the overall pressure ratio is the ratio of the final pressure to the inlet pressure:
$r_p=\frac{P_2}{P_1}$

Therefore, the final delivery pressure is:
$P_2=r_p\times P_1=6\times 100\text{kPa}=600\text{kPa}$

For minimum compressor work under ideal intercooling, the pressure ratio for each stage must be equal:
$\frac{P_i}{P_1}=\frac{P_2}{P_i}$

Solving this expression for the intermediate pressure $P_i$ yields:
${P_i}^2=P_1\times P_2$

Taking the square root of both sides gives:
$P_i=\sqrt{P_1\times P_2}$

Substituting the given values:
$P_i=\sqrt{100\times 600}=\sqrt{60000}\approx 244.95\text{kPa}$

Thus, rounding off to two decimal places, the optimum intercooling pressure for minimum compressor work is 244.94 kPa (or 244.95 kPa).