# Explanation of MECH 315 – Thermodynamics with Lab Homework 2 Let’s break down each problem and discuss the key concepts you’ll need to solve them. --- ## **2.1 Property Determination and T-v Diagram** For each subpart, you are given two properties of a substance (like **v** and **p** for water, or **p** and **T** for propane). Using the property tables (steam tables, refrigerant tables, etc.), you are to: 1. **Find the Required Property:** - Use the given information to look up (or interpolate) the unknown property in the appropriate thermodynamic tables. 2. **Locate the State:** - Sketch the state on a Temperature vs. specific volume (**T-v**) diagram. ### **Example:** **a) Water at \( v = 0.5 \frac{m^3}{kg}, p = 3\, bar \):** - Use the steam tables at \( p = 3\, bar \) to find the temperature corresponding to \( v = 0.5 \frac{m^3}{kg} \). - Check if this value lies in the compressed liquid, saturated mixture, or superheated region. --- ## **2.2 Rigid Tank with Refrigerant 134a** - **Closed, Rigid Tank:** Volume is constant. - **Given:** Initial two-phase mixture, initial and final temperatures, and pressures. - **Quality (x):** Percentage of vapor in the mixture. - **Procedure:** 1. Find initial and final states using refrigerant tables. 2. Use quality and specific volumes to find the mass of vapor. 3. Sketch both states on the T-v diagram. --- ## **2.3 Piston-Cylinder, Ammonia Compression (pV = constant)** - **Ammonia is compressed:** Temperature and pressure change. - **pV = constant:** This is a **polytropic process** with n = -1. - **Work and Heat Transfer:** Use first law of thermodynamics. - **Procedure:** 1. Find properties at initial and final states using ammonia tables. 2. Use the relationship for work in polytropic processes. 3. Apply energy balance to find heat transfer. --- ## **2.4 Piston-Cylinder, H₂O Two-Phase Mixture, Expansion** - **Two-phase mixture expands at constant pressure** until a final temperature is reached. - **Given Quality:** Initial state is a mixture; use tables to find properties. - **Procedure:** 1. Find initial state properties using quality and pressure. 2. Final state: use pressure and temperature to find final properties. 3. Use energy balance to determine work done. --- ## **2.5 Rigid, Closed Tank—Solar Heating** - **Rigid Tank:** Volume is constant, so mass is constant. - **Refrigerant is heated by the sun:** Temperature and pressure change. - **Key Steps:** 1. Initial state: use mass and volume to find initial specific volume and look up properties. 2. Final state: use pressure to find properties at saturated vapor. 3. Use energy balance to find heat transfer. --- ## **Key Concepts and Tools** - **Thermodynamic tables:** Steam tables, refrigerant tables, property charts. - **First Law of Thermodynamics:** \[ \Delta U = Q - W \] - **Quality (x) in Two-Phase Mixtures:** \[ x = \frac{m_{vapor}}{m_{total}} \] - **Rigid Tank:** Volume does not change. - **Constant Pressure/Volume Processes:** Know how to handle work and energy balance. - **T-v Diagram:** A plot used to visualize states and phase changes. --- ## **Tips** - Always identify the phase (compressed liquid, saturated mixture, superheated vapor) first. - Use **interpolation** if your values are between table entries. - Sketch T-v diagrams for visualization. - Clearly state assumptions (e.g., negligible kinetic and potential energy changes). --- ### **If you want to see a detailed solution for any specific problem, let me know which one!**