Math Problem Statement
H2O at 10 kPa, with h = 1500 kJ/kg; find x, T and s
Solution
To solve this problem, we are dealing with water (H₂O) under a pressure of 10 kPa and with a specific enthalpy (h) of 1500 kJ/kg. We need to find the quality (x), temperature (T), and specific entropy (s).
Step 1: Locate the state
We know the enthalpy , and pressure . This is low pressure, so it’s likely a saturated or superheated condition. First, let’s check the saturation properties of water at 10 kPa.
From steam tables:
- Saturation temperature at 10 kPa: 45.81°C
- Saturation enthalpy for liquid at 10 kPa: 191.81 kJ/kg
- Saturation enthalpy for vapor at 10 kPa: 2583.9 kJ/kg
Step 2: Determine the quality (x)
If the given enthalpy is within the range between and , the water is in the saturated mixture region, and we can find the quality using:
Rearranging to solve for :
Substitute the known values:
Thus, the quality , meaning the water is about 54.7% vapor and 45.3% liquid.
Step 3: Determine the temperature (T)
Since the water is a saturated mixture, the temperature is equal to the saturation temperature at the given pressure. From the steam tables:
Step 4: Determine the specific entropy (s)
Now that we know the quality , we can calculate the specific entropy using:
From steam tables at 10 kPa:
- Saturation entropy for liquid
- Saturation entropy for vapor
Substitute the values:
Thus, the specific entropy .
Final Answers:
- Quality (x):
- Temperature (T):
- Specific entropy (s):
Would you like further clarification on any step or details?
Here are 5 questions to expand your understanding:
- What happens to the quality when the enthalpy increases at the same pressure?
- How would the state change if the pressure were decreased further?
- How do you determine if water is in the superheated region?
- Why is the specific entropy important in thermodynamic processes?
- How would the temperature change if the quality of the mixture were increased?
Tip: Always check if the given enthalpy lies within the saturation region to determine the state of the water (liquid, mixture, or vapor).
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Math Problem Analysis
Mathematical Concepts
Thermodynamics
Enthalpy
Quality of a Mixture
Entropy
Formulas
x = (h - h_f) / (h_g - h_f)
T = T_sat
s = s_f + x * (s_g - s_f)
Theorems
Saturation Properties of Water
Thermodynamic Property Relations
Suitable Grade Level
College Level (Engineering or Physics)
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