Question

In a multistage compressor, intercooling is done to:

• A. Cool the air during compression
• B. Cool the air at delivery
• C. Enable compression in two stages
• D. Minimise the work of compression

Hint:

Think about the P-V diagram of compression. Cooling the gas between stages reduces its volume at the start of the next stage, thus reducing the area under the compression curve and hence the work done.

Answer 1

The Correct Option is D

Step 1: Understand the process of multistage compression. 
Multistage compression involves compressing a gas in two or more stages with cooling between the stages (intercooling). This is done to improve efficiency, especially for high pressure ratios. 
Step 2: Analyze the work of compression in a single stage. 
The work done to compress a gas depends on the process (isothermal, adiabatic, polytropic) and the pressure ratio. For a given pressure ratio, isothermal compression requires the least work, followed by polytropic, and then adiabatic requiring the most. In a single-stage compressor with a high pressure ratio, the temperature of the gas rises significantly, leading to higher work input. 
Step 3: Explain the role of intercooling in multistage compression. 
Intercooling involves cooling the gas after each stage of compression before it enters the next stage. The primary purpose of intercooling is to reduce the temperature of the gas, bringing it closer to the initial intake temperature. 
Step 4: Analyze how intercooling affects the work of compression. 
By reducing the temperature of the gas between stages, the density of the gas increases (according to the ideal gas law, \( PV = nRT \), so \( \rho = n/V = P/(RT) \)). A higher density means that for the same mass flow rate, the volume flow rate is lower. Consequently, the work required for compression in the subsequent stage is reduced because the work done in a compressor is related to the volume handled. Ideally, perfect intercooling cools the gas back to the initial intake temperature. In this case, for a given overall pressure ratio, the total work done in a multistage compressor with perfect intercooling is less than the work done in a single-stage compressor achieving the same pressure ratio. This is because the compression process in each stage starts at a lower temperature (or closer to the initial temperature), thus reducing the area under the P-V diagram for each stage and consequently the total work input. 
Step 5: Evaluate the given options. 
Option 1 (Cool the air during compression): Intercooling happens between the compression stages, not during a single stage of compression itself.
Option 2 (Cool the air at delivery): While the final temperature at delivery might be lower in a multistage compressor with intercooling compared to a single-stage compressor with the same pressure ratio, the primary purpose of intercooling is not solely to cool the air at the final delivery. After the last stage, further cooling might be done if required for the application.
Option 3 (Enable compression in two stages): Multistage compression is done for high pressure ratios, and intercooling is a beneficial aspect of it, but it's not the sole reason why compression is done in multiple stages. Multiple stages are used to keep the pressure ratio in each stage manageable.
Option 4 (Minimise the work of compression): This is the main thermodynamic reason for using intercooling in a multistage compressor. By reducing the temperature between stages, the work required for the subsequent compression stages is reduced, leading to a lower total work input for a given overall pressure ratio.
Step 6: Select the correct answer. 
The primary reason for intercooling in a multistage compressor is to minimise the work of compression.