In an ideal Brayton cycle, air is compressed from 84 kPa and 25C to 840 kPa. Under cold air standard conditions, the thermal efficiency of this cycle isQuestion 3Select one:a.48%b.52%c.10%d.60%e.74%
Question
In an ideal Brayton cycle, air is compressed from 84 kPa and 25C to 840 kPa. Under cold air standard conditions, the thermal efficiency of this cycle isQuestion 3Select one:a.48%b.52%c.10%d.60%e.74%
Solution
The thermal efficiency of an ideal Brayton cycle can be calculated using the formula:
η = 1 - (P2/P1)^((γ-1)/γ)
where: η is the thermal efficiency, P1 is the initial pressure, P2 is the final pressure, and γ (gamma) is the heat capacity ratio, which is approximately 1.4 for air.
Given in the problem: P1 = 84 kPa, P2 = 840 kPa, and γ = 1.4.
Substituting these values into the formula, we get:
η = 1 - (840/84)^((1.4-1)/1.4) η = 1 - 10^0.286 η = 1 - 1.95 η = -0.95
However, efficiency cannot be negative. There seems to be a mistake in the calculation. The exponent should be negative because we are dealing with a compression process (P2 > P1). Let's correct this:
η = 1 - (84/840)^(0.4/1.4) η = 1 - 0.1^0.286 η = 1 - 0.516 η = 0.484
So, the thermal efficiency of the cycle is approximately 48%. Therefore, the correct answer is (a) 48%.
Similar Questions
In an ideal Brayton cycle with regeneration, air is compressed from 80 kPa and 10C to 400 kPa and 180C, is heated to 450C in the regenerator, and then further heated to 1200C before entering the turbine. Under cold air standard conditions, the effectiveness of the regenerator isQuestion 1Select one:a.26%b.42%c.65%d.57%e.94%
Consider an ideal Brayton cycle executed between the pressure limits of 1100 kPa and 100 kPa and temperature limits of 20 deg C and 1200 deg C with argon (k = 1.667, cp = 0.5203 kJ/kg.K) as the working fluid. The net work output of the cycle isQuestion 10Select one:a.136 kJ/kgb.96 kJ/kgc.227 kJ/kgd.439 kJ/kge.456 kJ/kg
Air in an ideal Diesel cycle is compressed from 4 L to 0.25 L, and then it expands during the constant pressure heat addition process to 0.50 L. Under cold air standard conditions, the thermal efficiency of this cycle isQuestion 10Select one:a.49.0%b.38.6%c.61.4%d.67.0%e.79.5%
In an ideal Otto cycle, air is compressed from 1.15 kg/m3 and 2.2 L to 0.26 L, and the net work output of the cycle is 620 kJ/kg. The mean effective pressure (MEP) for this cycle isQuestion 8Select one:a.713 kPab.807 kPac.638 kPad.96 kPae.367 kPaClear my choiceCheckQuestion 8
Consider a gas turbine that has a pressure ratio of 8 and operates on the Brayton cycle with regeneration between the temperature limits of 20 deg C and 900 deg C. If the specific heat ratio of the working fluid is 1.33, the highest thermal efficiency this gas turbine can have isQuestion 4Select one:a.42%b.49%c.58%d.63%e.69%
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.