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 P₂ = 600kPa and the temperature is T=390K. The power input is W=5000kW and the heat loss rate is Q = 1000k//s during 1 2 out 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 P specific heat ratio k == 1.667, which means that enthalpy can be calculated using h=c_T. Calculate the enthalpy per unit mass at the P C exit h kJ/kg

Elements Of Electromagnetics
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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  .  Calculate the enthalpy per unit mass at the exit   _________ 

**Helium Compression Analysis**

Helium is compressed through a compressor steadily. At the inlet, the pressure is \( P_1 = 100 \, \text{kPa} \) and the temperature is \( T_1 = 300 \, \text{K} \). At the exit, the pressure is \( P_2 = 600 \, \text{kPa} \) and the temperature is \( T_2 = 390 \, \text{K} \). 

The system has a power input of \( \dot{W} = 5000 \, \text{kW} \) and the heat loss rate is \( \dot{Q}_{\text{out}} = 1000 \, \text{kJ/s} \) during this process. Neglect the kinetic and potential energy changes.

Assumptions:
- The helium behaves as an ideal gas.
- Constant specific heat \( c_p = 5.1926 \, \text{kJ/kg} \cdot \text{K} \).
- Specific heat ratio \( k = \frac{c_p}{c_v} = 1.667 \).

Using the relation \( h = c_p \cdot T \), you are to calculate the enthalpy per unit mass at the exit.

**Calculation:**
Determine the enthalpy \( h_2 \) in \(\text{kJ/kg}\).

\[
h_2 = \underline{\hspace{3cm}} \, \text{kJ/kg}
\]

**Use the provided data and equations to find \( h_2 \).**
Transcribed Image Text:**Helium Compression Analysis** Helium is compressed through a compressor steadily. At the inlet, the pressure is \( P_1 = 100 \, \text{kPa} \) and the temperature is \( T_1 = 300 \, \text{K} \). At the exit, the pressure is \( P_2 = 600 \, \text{kPa} \) and the temperature is \( T_2 = 390 \, \text{K} \). The system has a power input of \( \dot{W} = 5000 \, \text{kW} \) and the heat loss rate is \( \dot{Q}_{\text{out}} = 1000 \, \text{kJ/s} \) during this process. Neglect the kinetic and potential energy changes. Assumptions: - The helium behaves as an ideal gas. - Constant specific heat \( c_p = 5.1926 \, \text{kJ/kg} \cdot \text{K} \). - Specific heat ratio \( k = \frac{c_p}{c_v} = 1.667 \). Using the relation \( h = c_p \cdot T \), you are to calculate the enthalpy per unit mass at the exit. **Calculation:** Determine the enthalpy \( h_2 \) in \(\text{kJ/kg}\). \[ h_2 = \underline{\hspace{3cm}} \, \text{kJ/kg} \] **Use the provided data and equations to find \( h_2 \).**
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