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The single-stage compression process of an ideal Brayton cycle without regeneration is replaced by a multistage compression process with intercooling between the same pressure limits. As a result of this modification, (a) Does the compressor work increase, decrease, or remain the same? (b) Does the back work ratio increase, decrease, or remain the same? \((c) \quad\) Does the thermal efficiency increase, decrease, or remain the same?

Short Answer

Expert verified
Answer: Replacing a single-stage compression process with a multistage compression process with intercooling in an ideal Brayton cycle results in: (a) Decreased compressor work. (b) Decreased back work ratio. (c) Increased thermal efficiency.

Step by step solution

01

Understand the ideal Brayton Cycle

The ideal Brayton cycle consists of four processes: 1) Compression of the working fluid (air) in the compressor, 2) Constant pressure heat addition in the combustion chamber, 3) Expansion of the hot gases in the turbine, and 4) Constant pressure heat rejection from the working fluid in the exhaust. The thermal efficiency of the ideal Brayton cycle is given by \(\eta = 1- \frac{T_1 (T_3-T_2)}{(T_3-T_1)(T_2-T_1)}\), where \(T_1, T_2, T_3\) are the temperatures at the beginning of compression, end of compression, and end of heat addition processes, respectively.
02

Single-stage vs Multistage Compression

In a single-stage compression process, the working fluid is compressed in one step from an initial pressure to a final pressure. In a multistage compression process with intercooling, the compression is performed in multiple steps with cooling of the compressed fluid between each step, keeping the same initial and final pressure limits.
03

Compressor Work

In single-stage compression, the compressor work is given by \(W_c=T_1(p_2-p_1)\), where \(p_1\) and \(p_2\) represent the initial and final pressure before and after compression, respectively. On the other side, the multistage compressor work considering intercooling would be lesser than single-stage, as the cooling of compressed fluid reduces the work needed for further compression. So, the compressor work per unit mass, \(W_c\), decreases in the modified process. Thus, the answer for part (a) is that the compressor work decreases.
04

Back Work Ratio

The back work ratio in a Brayton cycle is the ratio of compressor work to turbine work, given by \(BWR = \frac{W_c}{W_t}\). For an ideal Brayton cycle, the turbine work per unit mass is given by \(W_t=T_3(p_3-p_4)\), where \(p_3\) and \(p_4\) represent the initial and final pressure before and after expansion, respectively. Since the multistage compression process with intercooling decreases the compressor work, the back work ratio also decreases. So, the answer for part (b) is that the back work ratio decreases.
05

Thermal Efficiency

As mentioned earlier, the thermal efficiency of the ideal Brayton cycle is given by \(\eta = 1- \frac{T_1 (T_3-T_2)}{(T_3-T_1)(T_2-T_1)}\). Due to the decrease in compressor work in the multistage compression process with intercooling, the numerator of the efficiency equation will be reduced. Since the denominator remains the same, the overall thermal efficiency will increase. So, the answer for part (c) is that the thermal efficiency increases. In conclusion, by replacing a single-stage compression process with a multistage compression process with intercooling in an ideal Brayton cycle: (a) The compressor work decreases. (b) The back work ratio decreases. (c) The thermal efficiency increases.

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An ideal diesel engine has a compression ratio of 20 and uses air as the working fluid. The state of air at the beginning of the compression process is \(95 \mathrm{kPa}\) and \(20^{\circ} \mathrm{C}\). If the maximum temperature in the cycle is not to exceed \(2200 \mathrm{K}\) determine \((a)\) the thermal efficiency and \((b)\) the mean effective pressure. Assume constant specific heats for air at room temperature.

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A simple ideal Brayton cycle is modified to incorporate multistage compression with intercooling, multistage expansion with reheating, and regeneration without changing the pressure limits of the cycle. As a result of these modifications, (a) Does the net work output increase, decrease, or remain the same? (b) Does the back work ratio increase, decrease, or remain the same? \((c) \quad\) Does the thermal efficiency increase, decrease, or remain the same? (d) Does the heat rejected increase, decrease, or remain the same?

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