Thermodynamics Exam Cheat Sheet: Problem-Solving Recipes

🔹 Problem 1: Property Changes & T-s Sketch

(HW 9 Q1–Q3)
1a. Ideal-Gas Entropy Change

Statement: Air (ideal gas) in a piston-cylinder goes from State 1: T₁ = 350 K, p₁ = 100 kPa to State 2: T₂ = 550 K, p₂ = 700 kPa. Find Δs (kJ/kg·K) (a) reversible, (b) with irreversibilities.

1b. Isothermal Water Compression

Statement: 1 kg water in a piston-cylinder, initially saturated vapor at T = 160 °C, p = 150 kPa, isothermally compressed to saturated liquid. Work on water W = -471.5 kJ. Find (a) Q (kJ), (b) ΔS (kJ/K). Sketch T-s.

Steps for 1a (Ideal Gas)

1. Formula:

   

2. Compute

   • 

3. Evaluate

   

4. Irreversible:

   

Steps for 1b (Water Compression)

1. 1st Law:

   

2. Table Lookup at 160 °C (saturated):

   • 

3. Compute ΔU:

   

4. Compute

Force Comparison Table

Zaha Hadid was designing the BMW Central Building.

The eventuality described in the VP ‘design the BMW Central Building” is [-static, +durative, +telic], thus an accomplishment. As shown in this example, it is compatible with the progressive, which emphasizes the progress of a [+durative] eventuality. Three diagnostics can be used to show that this event is an accomplishment, not an activity:

1. It is compatible with in-PPs ('Zaha Hadid designed the BMW Central Building in three months.'), but not with for-PPs ('Zaha Hadid designed the BMW Central Building in three months').
2. It does not have the sub-interval property: A subinterval of the event described in ‘Zaha Hadid designed the BMW Central Building’ cannot be described as ‘Zaha Hadid

Report N° 2: Physics Laboratory II

Electric Field and Potential

Concepción, April 13, 2009

Members:

• Carla Cáceres
• Jorge Gonzalez
• Fabián Soto

Teacher:

• Alberto Inostroza

Assistant:

• Raul Augurto

Objectives

• Determine how to map electric potential in a plane and draw equipotential lines.
• Derive the form of the electric field charge distribution in the plane from the equipotential lines diagram.

Materials

• Graph paper
• Glass cuvette
• Cables
• Voltmeter
• Multimeter
• Water
• Support

Setup

After verifying the materials were in good condition, the work platform was assembled. The glass cuvette was filled with approximately 3-4 mm of water. A sheet of graph paper was placed beneath the cuvette, aligned so that the gridlines were straight. Using the support, the positive and negative...

Material Constants

In addition to external dimensions and loads, material constants such as Young's modulus (E), Kirchhoff's modulus of elasticity (G), and Poisson's ratio (v) are essential for calculating strain and stress in structural components.

Young's Modulus (E)

Young's modulus, also known as the modulus of elasticity or linear deformation modulus, measures a material's stiffness in tension and compression. It expresses the relationship between the stress (σ) and the relative linear deformation (ε) within the range of elastic deformations.

Conceptually, Young's modulus represents the hypothetical stress required to double the length of a material, assuming its cross-section remains constant (a condition satisfied when Poisson's ratio equals...

The Governor is the nominal head (constitutional head) of a state in India, appointed by the President of India under Article 155 of the Constitution. Though modeled on the President at the Union level, the Governor functions mainly on the aid and advice of the State Council of Ministers, headed by the Chief Minister.

Constitutional Powers of the State Governor

The powers of the Governor can be classified into the following categories:

1. Executive Functions and Appointments

• Appoints the Chief Minister and other ministers (Article 164).
• Appoints the Advocate General, State Election Commissioner, and the Chairman and Members of the State Public Service Commission.
• Administers the oaths of office to various officials.
• Acts as the Chancellor of state

Motion and Force Formulas

• Speed = Distance ÷ Time (Distance in m, Time in s)
• Acceleration = Change in velocity ÷ Time (Velocity in m/s, Time in s)
• Force = Mass × Acceleration (Mass in kg, Acceleration in m/s²)
• Weight = Mass × Gravitational field strength (g = 9.8 N/kg)

Density and Energy Equations

• Density = Mass ÷ Volume (Mass in kg, Volume in m³)
• Kinetic Energy (KE) = ½ × Mass × Speed² (Mass in kg, Speed in m/s)
• Gravitational Potential Energy (GPE) = Mass × g × Height (Mass in kg, Height in m)
• Work Done = Force × Distance (Force in N, Distance in m)
• Power = Energy transferred ÷ Time (Energy in J, Time in s)
• Efficiency = (Useful energy output ÷ Total energy input) × 100%

Waves, Electricity, and Pressure

• Wave speed = Frequency × Wavelength

Young's Double Slit Experiment (YDSE)

Concept: In 1801, Thomas Young performed an experiment where he passed light through two narrow slits and observed an interference pattern on a screen. This pattern consists of alternating bright and dark fringes.

Experimental Setup

• Monochromatic Light: Light of a single wavelength falls on a primary slit S.
• Slit Arrangement: From slit S, light travels to two secondary slits, S₁ and S₂.
• Diffraction and Interference: Light diffracts from S₁ and S₂ and interferes on the screen.
• Constructive Interference: This occurs where waves meet in phase, resulting in a bright fringe.
• Destructive Interference: This occurs where waves meet out of phase, resulting in a dark fringe.

Fringe Width Derivation (W)

Let:

• D = Distance between

Kirchhoff’s Current Law (KCL)

Statement:

At any junction (node) in an electrical circuit, the algebraic sum of currents is zero

∑ I=0

Explanation:

• At a junction, current cannot accumulate.

• Therefore, the total current entering must be equal to the total current leaving.

Example:
If currents I1I_1I1​ and I2I_2I2​ enter a node and I3I_3I3​ and I4I_4I4​ leave:     I1​+I2​=I3​+I4​  

2) Kirchhoff’s Voltage Law (KVL)

Statement:

In any closed loop of an electrical circuit, the algebraic sum of all voltages is zero.

∑V=0

Explanation:

• While moving around a closed loop, the sum of voltage rises equals the sum of voltage drops.

• This law is based on the conservation of energy.

Example:
For a loop with a source EEE and voltage drops V1​,V2​:...

Dielectric Polarization and Its Mechanisms

Dielectric Polarization: When a dielectric (insulating) material is placed in an external electric field, its positive and negative charges shift slightly from their equilibrium positions. This induces temporary dipole moments within the material, a process known as dielectric polarization.

Electronic Polarization

This occurs when the applied electric field displaces the negatively charged electron cloud of an atom relative to its positively charged nucleus. It occurs in all dielectric materials. It is a very rapid process and is independent of temperature.

Orientation Polarization

This occurs only in materials composed of molecules that have permanent dipole moments (like H₂O). Normally, these dipoles...