Physics Exam 3 Definitions and Derivations
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Questions and Answers

What is defined as the state where a material exists simultaneously as a solid, liquid, and gas?

  • Triple point (correct)
  • Phase boundary
  • Critical point
  • Equilibrium point

What does the equation $W = \int_{V_1}^{V_2} p dV$ represent?

  • Work done during a volume change (correct)
  • Work done during a pressure change
  • Work done during a phase transition
  • Work done during a temperature change

What describes the First Law of Thermodynamics?

  • dU = dQ - dW
  • U = Q - W
  • U = Q + W
  • dU = dQ + dW (correct)

How is the relationship between molar heat capacities expressed?

<p>C_P = C_V + R (C)</p> Signup and view all the answers

In an isothermal process, which statement is true?

<p>The temperature remains constant and the internal energy stays constant. (C)</p> Signup and view all the answers

What is the outcome during an adiabatic process?

<p>The internal energy changes due to work done. (B)</p> Signup and view all the answers

Which of the following thermodynamic processes involves a constant volume?

<p>Isochoric (B)</p> Signup and view all the answers

What characterizes a pV diagram?

<p>Shows how pressure changes with volume at constant temperature. (C)</p> Signup and view all the answers

What molecular behavior explains the expansion of objects with temperature increases?

<p>Molecules gain motion and occupy more space. (D)</p> Signup and view all the answers

Which experiment was foundational in linking heat and energy?

<p>Joule's experiment. (C)</p> Signup and view all the answers

What does specific heat represent?

<p>The heat required to raise the temperature of a substance by one degree. (B)</p> Signup and view all the answers

Which formula represents the average translational kinetic energy per gas molecule?

<p>(1/2)m(v^2)avg = (3/2)k_B T (D)</p> Signup and view all the answers

What is the ideal gas law equation?

<p>pV = nRT (C)</p> Signup and view all the answers

What is Avogadro's number approximately equal to?

<p>6.022 x 10^23 mol^-1 (A)</p> Signup and view all the answers

What does the Maxwell-Boltzmann velocity distribution describe?

<p>The distribution of speeds among gas molecules. (C)</p> Signup and view all the answers

What is the molar heat capacity at constant volume for an ideal monatomic gas?

<p>(3/2)R (D)</p> Signup and view all the answers

What is the relationship between total mass and moles?

<p>Total mass equals the number of moles multiplied by the molar mass. (A)</p> Signup and view all the answers

What unit is used to express Boltzmann's constant ($k_B$)?

<p>J/molecule · K (D)</p> Signup and view all the answers

How is the number of moles calculated?

<p>By dividing total molecules by Avogadro's number. (C)</p> Signup and view all the answers

What does the mean free path equation represent?

<p>Distance traveled by a particle before colliding. (B)</p> Signup and view all the answers

What is the significance of the area under a pV-diagram?

<p>It represents the work done by the gas. (C)</p> Signup and view all the answers

Which of the following is NOT a characteristic of the kinetic-molecular model?

<p>Molecules have inelastic collisions with the walls. (A)</p> Signup and view all the answers

What does $m_{molecule}$ represent in the context of molecular mass?

<p>Mass of a single molecule calculated as $M/N_A$. (D)</p> Signup and view all the answers

What is the formula to calculate the total mass of a substance?

<p>$m_{total} = nM$ (B)</p> Signup and view all the answers

What is the relationship between the ratio of two Kelvin temperatures and the corresponding pressures in a constant-volume gas thermometer?

<p>$T_2/T_1 = p_2/p_1$ (D)</p> Signup and view all the answers

What is the equation for thermal expansion in solids?

<p>$V = ²V_0 T$ (C)</p> Signup and view all the answers

Which formula correctly describes the quantity of heat required to change the temperature of a certain mass?

<p>$Q = mcT$ (B)</p> Signup and view all the answers

What is the equation for heat transfer during a phase change?

<p>$Q = mL$ (C)</p> Signup and view all the answers

What defines the condition for thermal equilibrium between two systems?

<p>The same temperature (D)</p> Signup and view all the answers

As temperature increases, what happens to pressure in a constant-volume gas thermometer?

<p>Pressure increases proportionally (D)</p> Signup and view all the answers

What temperature corresponds to absolute zero on the Kelvin scale?

<p>0 K (B)</p> Signup and view all the answers

How do Celsius and Kelvin scales relate in terms of temperature changes?

<p>They both increase/decrease at the same rate (C)</p> Signup and view all the answers

What happens to the change in internal energy for a cyclic process?

<p>It equals zero (C)</p> Signup and view all the answers

What is the formula for thermal efficiency of a heat engine?

<p>e = W/Q_H (A)</p> Signup and view all the answers

In a closed system, what can be said about the net heat transfer and work done?

<p>Q = 0, W = 0 (C)</p> Signup and view all the answers

What does the coefficient of performance (K) indicate for a refrigerator?

<p>Effectiveness in removing heat (B)</p> Signup and view all the answers

According to the second law of thermodynamics, what is the change in entropy (S) during a reversible process?

<p>S &gt; 0 (C)</p> Signup and view all the answers

Which statement accurately describes irreversible processes?

<p>They can only occur in the forward direction (D)</p> Signup and view all the answers

What equation describes the efficiency of a Carnot engine?

<p>e_Carnot = 1 - (T_C/T_H) (C)</p> Signup and view all the answers

What is the condition for internal energy change (U) in an isolated system?

<p>U = 0 (B)</p> Signup and view all the answers

What does the average translational kinetic energy for an ideal gas depend on?

<p>Temperature and number of moles (D)</p> Signup and view all the answers

What is the equation derived for the average velocities of all molecules present in a gas?

<p>v^2 = v_x^2 + v_y^2 + v_z^2 (A)</p> Signup and view all the answers

How is pressure related to the translational kinetic energy of a gas according to the model?

<p>pV = (1/3)Nm(v^2)_avg (A)</p> Signup and view all the answers

What is the definition of the 'mean free time' in a gas?

<p>The average time between particle collisions (B)</p> Signup and view all the answers

What does the Maxwell-Boltzmann distribution describe?

<p>The spread of molecular speeds in a gas (A)</p> Signup and view all the answers

What is the mean free path in the context of gas particles?

<p>The average distance a particle travels between collisions (C)</p> Signup and view all the answers

In the equation pV = (2/3)K_translational, what does K_translational represent?

<p>Average translational kinetic energy (A)</p> Signup and view all the answers

Which of the following assumptions is made in the Kinetic-Molecular Model about the container walls?

<p>They are perfectly rigid and infinitely large (B)</p> Signup and view all the answers

Flashcards

Kelvin Temperature

A temperature scale where zero is absolute zero, the point at which all molecular motion stops.

Thermal Equilibrium

When two systems have the same temperature, and there's no net heat flow between them

Constant-Volume Gas Thermometer

A thermometer that measures temperature by monitoring the pressure of a gas kept at a constant volume.

Zeroth Law of Thermodynamics

If two systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other

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Temperature

A measure of the average kinetic energy of particles in a substance.

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Specific Heat

The amount of heat required to raise the temperature of one gram of a substance by one degree Celsius.

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Heat of Fusion/Vaporization

The amount of heat required to change a substance from solid to liquid or liquid to gas (at constant temperature).

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Relationship of Temperature Scales

Celsius and Kelvin increase/decrease at the same rate, while Fahrenheit is different . Freezing water (0°C, 32°F, 273.15 K), and boiling water (100°C, 212°F, 373.15 K)

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Molecular Basis of Expansion/Contraction

Increased molecular motion at higher temperatures leads to greater space occupied by molecules, causing expansion. Conversely, lower temperatures result in less molecular movement and reduced space, causing contraction.

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Joule's Experiment Significance

Joule's experiments demonstrated the equivalence of heat and mechanical work/energy, forming the basis of the Law of Conservation of Energy. This laid the groundwork for thermodynamics.

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Specific Heat Definition

The amount of heat energy needed to raise the temperature of a unit mass of a substance by one degree.

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Calorimetry Problem Solving

Identify temperature/phase changes, assign variables, and set the sum of heat energies equal to zero (energy is conserved).

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Ideal Gas Law Formula

pV = nRT (with R as the gas constant), where p is pressure, V is volume, n is moles, R is constant, and T is temperature.

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Average Translational KE

The average kinetic energy per gas molecule is (1/2)m(v²).avg = (3/2)kBT

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RMS Speed Formula

The root-mean-square speed of a gas molecule is v_rms = sqrt((v^2)avg).

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Molar Heat Capacities (ideal gas)

The molar heat capacity at constant volume for a monatomic ideal gas is C_V = (f/2)R or 3/2 k_B T. For an ideal monatomic solid, it's C_V = 3R.

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Relationship between mass, molar mass, moles, and molecules

Total mass (m) equals the number of moles (n) times the molar mass (M). A mole contains Avogadro's number (N_A) of molecules. A molecule's mass (m_molecule) is the molar mass (M) divided by Avogadro's number (N_A).

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Kinetic-Molecular Model Assumptions

The kinetic-molecular model assumes that gas molecules are point particles, constantly moving, and experiencing elastic collisions among themselves and the container walls.

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Total mass

The total amount of mass within a substance.

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Molar mass

The mass of one mole of a substance.

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Number of moles

Quantifies the amount of a substance.

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Number of molecules

The count of individual molecules in a substance (6.022 x 10^23 molecules per mole).

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pV-diagrams

Graphs showing the relationship between pressure (p) and volume (V) during a gas process. The area under the curve represents the work done by the gas.

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Boltzmann constant (k_B)

A fundamental constant relating energy to temperature. k_B = R/N_A (where R = ideal gas constant, N_A = Avogadro's number).

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Mass of an individual molecule (m_molecule)

The mass of a single molecule, calculated as the molar mass divided by Avogadro's number.

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Average Translational Kinetic Energy (Ideal Gas)

The average amount of kinetic energy possessed by the particles in a gas, directly related to the temperature.

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Mean Free Time

Average time between collisions of gas particles.

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Mean Free Path

The average distance a gas particle travels between collisions.

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Maxwell-Boltzmann Distribution

Describes the distribution of speeds of gas particles in a gas at a given temperature.

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Ideal Gas Law (equation)

pV = nRT, relating pressure, volume, amount of gas, and temperature.

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pVT-surface

A 3D representation showing the relationship between gas pressure, volume, and temperature.

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Kinetic-Molecular Model (Assumption)

Gas' particles' speed, and the container's size are considered. Perfectly rigid and infinitely large.

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Average Translational KE Formula

(3/2)nRT

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pVT-Surface

A 3D graph showing the relation between pressure (p), volume (V), and temperature (T) for a material.

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Triple Point

The specific temperature and pressure where a substance can exist as solid, liquid, and gas simultaneously.

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Work Done (Volume Change)

The integral of pressure with respect to volume (from initial to final) during a process.

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First Law of Thermodynamics

The change in internal energy equals the heat added minus the work done.

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Isochoric Process

Constant volume process; no work is done.

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Isobaric Process

Constant pressure process; work is directly proportional to volume change.

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Isothermal Process

Constant temperature process; change in internal energy is zero, so heat added equals work done.

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Adiabatic Process

No heat transfer in or out of the system, thus change in internal energy = work done.

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Cyclic Process Internal Energy

The total internal energy change for a cyclic process is zero.

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Isolated System Energy

In an isolated system, there is no interaction with surroundings (Q=0 and W=0), so the change in internal energy (∆U) is zero.

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Heat Engine Definition

A device that converts heat energy into work or mechanical energy.

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pV Diagram Work

The area under the curve on a pV diagram represents the work done by the gas.

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Thermodynamic Process Formula

Change in internal energy (∆U) = heat (Q) – work (W) or ∆U = Q – W.

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Heat Engine Efficiency

The ratio of work output to heat input: efficiency = work/heat input or e = W/QH (where QH is the heat absorbed from the high-temperature reservoir).

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Reversible Process

A process that can occur both forwards and backwards naturally.

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Irreversible Process

A process that can only occur in one direction naturally (e.g., all real-world thermodynamic processes).

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Study Notes

Exam 3 Definitions and Derivations

  • Ratio of Kelvin temperatures and pressures (constant-volume gas thermometer): (T₂/T₁) = (p₂/p₁)

  • Thermal expansion formulae: L = L₀(1 + αT), V = V₀(1 + βT) (for solids, β = 3α)

  • Heat required to change temperature: Q = mcΔT (c = specific heat), Q = nCΔT (C = molar heat capacity)

  • Heat transfer in a phase change: Q = ±mL (L = heat of fusion/vaporization/etc.)

  • Temperature: A measure of the average kinetic energy of particles in a substance (measured in K, F, or C).

  • Thermal equilibrium: Two systems are in thermal equilibrium if and only if they have the same temperature.

  • Constant-volume gas thermometer: Measures pressure, which is proportional to temperature using a constant volume.

  • Absolute zero: As pressure approaches 0, temperature approaches -273.15 K (absolute zero).

  • Temperature scales: Fahrenheit, Celsius, and Kelvin share relationships defined by the freezing and boiling points of water:

  • Freezing point of water: C = 0, F = 32, K = 273.15

  • Boiling point of water: C = 100, F = 212, K = 373.15

  • Expansion/contraction with temperature: Temperature changes correlate with changes in energy; higher temperatures mean more molecular motion and greater space occupied.

  • Joule's experiment significance: Demonstrated the equivalence of heat and mechanical energy, leading to the law of conservation of energy.

  • Specific heat: Amount of heat required to raise the temperature of a given mass of a substance by one degree.

  • Calorimetry problem solving: Identify changes (temperature/phase change), assign variables, and set the sum of all heat energies equal to zero (energy is conserved).

  • Ideal gas law equations: pV = nRT = Nk₂T; R = k₂Nₐ = 8.314 J/mol⋅K

  • Average translational kinetic energy per gas molecule: (1/2)mv²avg = (3/2)k₂T

  • Root-mean-square speed of a gas molecule: vrms = √((v²)avg)

  • Molar heat capacities: CV = (f/2)R for gases, CV = 3R for ideal monatomic solids (f is degrees of freedom)

  • Maxwell-Boltzmann velocity distribution: A probability distribution showing the speeds at which gas molecules move. f(v) = 4π(m/2πkT)3/2 v² e−mv²/2kT

  • Avogadro's number: Approximately 6.022 × 10²³ molecules/mol

  • Boltzmann constant: k₂ = R/Nₐ = 1.381 × 10⁻²³ J/molecule⋅K

  • Relationships between mass, molar mass, moles, and molecules: mtotal = nM, mmolecule = M/Nₐ, n = N/Nₐ

pV-Diagrams

  • Pressure on y-axis, Volume on x-axis: Visual representation of a gas's change in volume with pressure. Area under the curve equals the work done by the gas.

  • Characteristic processes (adiabatic, isothermal): Different processes are identified by their characteristics presented visually on a pV-diagram.

pVT-surfaces

  • Three-dimensional representation of pressure, volume, and temperature: Show relationships between pressure, volume and temperature. Cross-sections produce pT- and pV-diagrams.

Triple Point

  • Specific temperature and pressure condition: Where solid, liquid, and gas phases of a substance coexist.

Work Done In A Volume Change

  • W = ∫V1V2pdV: Formula to calculate the work done in a volume change.

First Law of Thermodynamics

  • U = Q - W

Thermodynamic Relationships

  • Molar Heat Capacities: Cp = Cv + R

  • Adiabatic Relationships: pVγ = constant

Thermodynamic System

A collection of objects capable of exchanging heat

Carnot Cycle

  • Isothermal expansion: Expanding gas at constant temperature, absorbing heat.

  • Adiabatic expansion: Expanding gas without heat exchange.

  • Isothermal compression: Compressing gas at low temperature, releasing heat.

  • Adiabatic compression: Compressing gas without heat exchange.

Free Expansion

  • Expanding gas into a vacuum: No work is required as there is no outside pressure.

Entropy

  • Measure of disorder/tendency towards disorder in a system: A naturally occurring process always accompanies an increase in entropy.

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