1 1 Helium is compressed through a compressor steadily. At the inlet the pressure is P₁ = 100kPa and the temperature is T₁ = 300K. At the exit the pressure is P₁= 600kPa and the temperature is T₂=390K. The power input is W = 5000kW and the heat loss rate is Q = 1000k.//s during this process. Neglect the kinetic and potential energy changes. Assume helium is ideal gas with a constant specific heat c=5.1926 kJ/kg-K and its out P P specific heat ratio k == 1.667, which means that enthalpy can be calculated using h=c_T. Select the simplified the energy balance equation C P for this process OA. V² (Q-Q_) + (WW) + [ Σm(h+ • [ m(h+ 1/ / / + - in in OB. _Q+W+m(h₁-h₂) = 0 in out D.Q out out OC. _Q-W + m(h₂-h₂) = 0 out out 1 out -W₁ +m(h₁-h₂) = 0 V2 +82) - Σm(h+- - out +gz)]= dE system dt
1 1 Helium is compressed through a compressor steadily. At the inlet the pressure is P₁ = 100kPa and the temperature is T₁ = 300K. At the exit the pressure is P₁= 600kPa and the temperature is T₂=390K. The power input is W = 5000kW and the heat loss rate is Q = 1000k.//s during this process. Neglect the kinetic and potential energy changes. Assume helium is ideal gas with a constant specific heat c=5.1926 kJ/kg-K and its out P P specific heat ratio k == 1.667, which means that enthalpy can be calculated using h=c_T. Select the simplified the energy balance equation C P for this process OA. V² (Q-Q_) + (WW) + [ Σm(h+ • [ m(h+ 1/ / / + - in in OB. _Q+W+m(h₁-h₂) = 0 in out D.Q out out OC. _Q-W + m(h₂-h₂) = 0 out out 1 out -W₁ +m(h₁-h₂) = 0 V2 +82) - Σm(h+- - out +gz)]= dE system dt
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question
Helium is compressed through a compressor steadily. At the inlet the pressure is and the temperature is . At the exit the pressure is and the temperature is . The power input is and the heat loss rate is during this process. Neglect the kinetic and potential energy changes. Assume helium is ideal gas with a constant specific heat and its specific heat ratio , which means that enthalpy can be calculated using . Select the simplified the energy balance equation for this process_________
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![**Helium Compression Process Analysis**
In this exercise, helium is compressed through a compressor operating steadily. The initial conditions at the inlet are a pressure \( P_1 = 100 \, \text{kPa} \) and a temperature \( T_1 = 300 \, \text{K} \). At the exit, the helium's pressure increases to \( P_2 = 600 \, \text{kPa} \) with a temperature of \( T_2 = 390 \, \text{K} \).
The system operates with the following energy parameters:
- Power input: \( \dot{W} = 5000 \, \text{kW} \)
- Heat loss rate: \( \dot{Q}_{out} = 1000 \, \text{kJ/s} \)
Assumptions include:
- Negligible changes in kinetic and potential energy.
- Helium behaves as an ideal gas with a constant specific heat, where \( c_p = 5.1926 \, \text{kJ/kg} \cdot \text{K} \).
- The specific heat ratio is \( k = \frac{c_p}{c_v} = 1.667 \).
Enthalpy can be calculated using the equation \( h = c_p \, T \).
**Problem Statement:**
Select the simplified energy balance equation for this process from the options given below.
**Options:**
A.
\[
(\dot{Q}_{in} - \dot{Q}_{out}) + (\dot{W}_{in} - \dot{W}_{out}) + \left[ \sum_{in} \dot{m} \left( h + \frac{V^2}{2} + gz \right) - \sum_{out} \dot{m} \left( h + \frac{V^2}{2} + gz \right) \right] = \frac{dE_{system}}{dt}
\]
B.
\[
-\dot{Q}_{out} + \dot{W}_{in} + \dot{m} (h_1 - h_2) = 0
\]
C.
\[
-\dot{Q}_{out} - \dot{W}_{out} + \dot{m} (h_1 - h_2) = 0
\]
D.
\[
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Transcribed Image Text:**Helium Compression Process Analysis**
In this exercise, helium is compressed through a compressor operating steadily. The initial conditions at the inlet are a pressure \( P_1 = 100 \, \text{kPa} \) and a temperature \( T_1 = 300 \, \text{K} \). At the exit, the helium's pressure increases to \( P_2 = 600 \, \text{kPa} \) with a temperature of \( T_2 = 390 \, \text{K} \).
The system operates with the following energy parameters:
- Power input: \( \dot{W} = 5000 \, \text{kW} \)
- Heat loss rate: \( \dot{Q}_{out} = 1000 \, \text{kJ/s} \)
Assumptions include:
- Negligible changes in kinetic and potential energy.
- Helium behaves as an ideal gas with a constant specific heat, where \( c_p = 5.1926 \, \text{kJ/kg} \cdot \text{K} \).
- The specific heat ratio is \( k = \frac{c_p}{c_v} = 1.667 \).
Enthalpy can be calculated using the equation \( h = c_p \, T \).
**Problem Statement:**
Select the simplified energy balance equation for this process from the options given below.
**Options:**
A.
\[
(\dot{Q}_{in} - \dot{Q}_{out}) + (\dot{W}_{in} - \dot{W}_{out}) + \left[ \sum_{in} \dot{m} \left( h + \frac{V^2}{2} + gz \right) - \sum_{out} \dot{m} \left( h + \frac{V^2}{2} + gz \right) \right] = \frac{dE_{system}}{dt}
\]
B.
\[
-\dot{Q}_{out} + \dot{W}_{in} + \dot{m} (h_1 - h_2) = 0
\]
C.
\[
-\dot{Q}_{out} - \dot{W}_{out} + \dot{m} (h_1 - h_2) = 0
\]
D.
\[
\
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