Math Problem Statement

EGR23 Examination I Property Tables(1).docx

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Solution

The document you uploaded contains an exam on thermodynamic property tables, with two main problems. Here’s a summary of the tasks:

Problem 1:

You are required to complete a thermodynamic property table for different states of water (H₂O) and refrigerant (R-134a). The table includes:

  • Pressure (P) in kPa
  • Temperature (T) in °C
  • Specific volume (v) in m³/kg
  • Internal energy (u) in kJ/kg
  • Enthalpy (h) in kJ/kg
  • Entropy (s) in kJ/(kg K)
  • Quality (x) (which is the ratio of vapor mass to total mass, used in two-phase mixtures)
  • Phase (either liquid, vapor, or two-phase mixture)

Problem 2:

You are asked to analyze a system with 3 kg of water in a piston-cylinder device at 30°C and 1.0 MPa. The water is heated at constant pressure until it reaches 400°C. The tasks include:

  1. P-v Diagram: Sketch a Pressure-specific volume diagram.
  2. T-v Diagram: Sketch a Temperature-specific volume diagram.
  3. Work Calculation: Determine the work done by the system during the process.
  4. Heat Transfer: Calculate the heat transferred to the system.

Would you like help solving these thermodynamic problems? Let me know if you want detailed guidance on any part of the exam. Here are some related questions that could help expand your understanding:

  1. How do you find thermodynamic properties from steam or refrigerant tables?
  2. What are the steps to calculate work in a constant pressure process for water?
  3. How is quality (x) calculated in a two-phase mixture?
  4. What is the relationship between specific enthalpy and heat transfer in a piston-cylinder system?
  5. How do you sketch a P-v or T-v diagram for thermodynamic processes?

Tip: When completing thermodynamic tables, always start by finding values in property tables for known pressures and temperatures. These tables help you interpolate when values are not explicitly given.

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Math Problem Analysis

Mathematical Concepts

Thermodynamic Properties
Heat Transfer
Work Done in Piston-Cylinder Systems

Formulas

Work = P * ΔV
Heat Transfer (Q) = m * Δh
Ideal Gas Law (for gases): PV = nRT
Quality (x) = (v - v_f) / (v_g - v_f) for two-phase mixtures

Theorems

First Law of Thermodynamics (Energy Conservation)
Thermodynamic Property Relationships

Suitable Grade Level

Undergraduate Thermodynamics or Engineering Course