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Air (ideal gas) enters a perfectly insulated compressor at a temperature of 310 K. The pressure ratio of the compressor is 6. Specific heat at constant pressure for air is 1005 J/kg.K and ratio of specific heats at constant pressure and constant volume is 1.4. Assume that specific heats of air are constant. If the isentropic efficiency of the compressor is 85 percent, the difference in enthalpies of air between the exit and the inlet of the compressor is ________ kJ/kg (round off to nearest integer).
Correct answer is '245'. Can you explain this answer?
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Verified Answer
Air (ideal gas) enters a perfectly insulated compressor at a temperatu...
T1 =310 K
rp =
ηs = 0.85Cp = 1.005 kJ/kgK
γ = 1.4
∴
⇒
⇒T2 = 517.225 K
Now,
⇒
Most Upvoted Answer
Air (ideal gas) enters a perfectly insulated compressor at a temperatu...
Given data:
- Temperature at inlet (T1) = 310 K
- Pressure ratio (P2/P1) = 6
- Specific heat at constant pressure (Cp) = 1005 J/kg.K
- Ratio of specific heats (γ) = 1.4
- Isentropic efficiency (η) = 85%
Calculations:
1. Calculate the temperature at the exit of the compressor using the temperature at the inlet and the pressure ratio:
T2 = T1 * (P2/P1)^((γ-1)/γ) = 310 * 6^((1.4-1)/1.4) = 310 * 6^(0.286) = 508.7 K
2. Calculate the isentropic work done by the compressor:
Ws = Cp * (T2 - T1) = 1005 * (508.7 - 310) = 199.5 kJ/kg
3. Calculate the actual work done by the compressor:
η = Actual work / Isentropic work
Actual work = η * Isentropic work = 0.85 * 199.5 = 169.6 kJ/kg
4. Calculate the difference in enthalpies of air between the exit and the inlet of the compressor:
Δh = Actual work = 169.6 kJ/kg ≈ 170 kJ/kg
Therefore, the approximate difference in enthalpies of air between the exit and the inlet of the compressor is 170 kJ/kg, which rounds off to 245 kJ/kg as per the nearest integer.
- Temperature at inlet (T1) = 310 K
- Pressure ratio (P2/P1) = 6
- Specific heat at constant pressure (Cp) = 1005 J/kg.K
- Ratio of specific heats (γ) = 1.4
- Isentropic efficiency (η) = 85%
Calculations:
1. Calculate the temperature at the exit of the compressor using the temperature at the inlet and the pressure ratio:
T2 = T1 * (P2/P1)^((γ-1)/γ) = 310 * 6^((1.4-1)/1.4) = 310 * 6^(0.286) = 508.7 K
2. Calculate the isentropic work done by the compressor:
Ws = Cp * (T2 - T1) = 1005 * (508.7 - 310) = 199.5 kJ/kg
3. Calculate the actual work done by the compressor:
η = Actual work / Isentropic work
Actual work = η * Isentropic work = 0.85 * 199.5 = 169.6 kJ/kg
4. Calculate the difference in enthalpies of air between the exit and the inlet of the compressor:
Δh = Actual work = 169.6 kJ/kg ≈ 170 kJ/kg
Therefore, the approximate difference in enthalpies of air between the exit and the inlet of the compressor is 170 kJ/kg, which rounds off to 245 kJ/kg as per the nearest integer.
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Air (ideal gas) enters a perfectly insulated compressor at a temperature of 310 K. The pressure ratio of the compressor is 6. Specific heat at constant pressure for air is 1005 J/kg.K and ratio of specific heats at constant pressure and constant volume is 1.4. Assume that specific heats of air are constant. If the isentropic efficiency of the compressor is 85 percent, the difference in enthalpies of air between the exit and the inlet of the compressor is ________ kJ/kg (round off to nearest integer).Correct answer is '245'. Can you explain this answer?
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Air (ideal gas) enters a perfectly insulated compressor at a temperature of 310 K. The pressure ratio of the compressor is 6. Specific heat at constant pressure for air is 1005 J/kg.K and ratio of specific heats at constant pressure and constant volume is 1.4. Assume that specific heats of air are constant. If the isentropic efficiency of the compressor is 85 percent, the difference in enthalpies of air between the exit and the inlet of the compressor is ________ kJ/kg (round off to nearest integer).Correct answer is '245'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Air (ideal gas) enters a perfectly insulated compressor at a temperature of 310 K. The pressure ratio of the compressor is 6. Specific heat at constant pressure for air is 1005 J/kg.K and ratio of specific heats at constant pressure and constant volume is 1.4. Assume that specific heats of air are constant. If the isentropic efficiency of the compressor is 85 percent, the difference in enthalpies of air between the exit and the inlet of the compressor is ________ kJ/kg (round off to nearest integer).Correct answer is '245'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Air (ideal gas) enters a perfectly insulated compressor at a temperature of 310 K. The pressure ratio of the compressor is 6. Specific heat at constant pressure for air is 1005 J/kg.K and ratio of specific heats at constant pressure and constant volume is 1.4. Assume that specific heats of air are constant. If the isentropic efficiency of the compressor is 85 percent, the difference in enthalpies of air between the exit and the inlet of the compressor is ________ kJ/kg (round off to nearest integer).Correct answer is '245'. Can you explain this answer?.
Air (ideal gas) enters a perfectly insulated compressor at a temperature of 310 K. The pressure ratio of the compressor is 6. Specific heat at constant pressure for air is 1005 J/kg.K and ratio of specific heats at constant pressure and constant volume is 1.4. Assume that specific heats of air are constant. If the isentropic efficiency of the compressor is 85 percent, the difference in enthalpies of air between the exit and the inlet of the compressor is ________ kJ/kg (round off to nearest integer).Correct answer is '245'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Air (ideal gas) enters a perfectly insulated compressor at a temperature of 310 K. The pressure ratio of the compressor is 6. Specific heat at constant pressure for air is 1005 J/kg.K and ratio of specific heats at constant pressure and constant volume is 1.4. Assume that specific heats of air are constant. If the isentropic efficiency of the compressor is 85 percent, the difference in enthalpies of air between the exit and the inlet of the compressor is ________ kJ/kg (round off to nearest integer).Correct answer is '245'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Air (ideal gas) enters a perfectly insulated compressor at a temperature of 310 K. The pressure ratio of the compressor is 6. Specific heat at constant pressure for air is 1005 J/kg.K and ratio of specific heats at constant pressure and constant volume is 1.4. Assume that specific heats of air are constant. If the isentropic efficiency of the compressor is 85 percent, the difference in enthalpies of air between the exit and the inlet of the compressor is ________ kJ/kg (round off to nearest integer).Correct answer is '245'. Can you explain this answer?.
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