Physics Chapter on Temperature and Heat
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Questions and Answers

What does the net radiation heat current depend on?

  • The area of the body only
  • The temperature of the body and the surroundings (correct)
  • The volume of the body only
  • Only the temperature of the surroundings

Which equation correctly represents the ideal-gas equation of state?

  • pV = nRT (correct)
  • pV/T = nR
  • p = nRT/V
  • V = nRT/p

How is the total translational kinetic energy of an ideal gas represented?

  • Ktr = 3nRT
  • Ktr = nRT/3
  • Ktr = 3nRT/2 (correct)
  • Ktr = 2nRT/3

What is the root-mean-square speed of the molecules in an ideal gas given by?

<p>vrms = sqrt(3kT/m) (C)</p> Signup and view all the answers

What does Avogadro's number represent?

<p>The number of molecules in a mole (B)</p> Signup and view all the answers

What is the maximum coefficient of performance (K) of a refrigerator operating between two temperatures compared to a Carnot refrigerator?

<p>It can be less than that of a Carnot refrigerator. (D)</p> Signup and view all the answers

Which formula represents the change in entropy (∆S) for a reversible process?

<p>∆S = dQ / T (B)</p> Signup and view all the answers

What happens to the total entropy of an isolated system over time?

<p>It may increase but can never decrease. (A)</p> Signup and view all the answers

How does the total entropy of a system and its surroundings change when irreversible processes occur?

<p>The total entropy increases. (B)</p> Signup and view all the answers

What condition applies to the total entropy when only reversible processes are involved?

<p>The total entropy is constant, ∆S = 0. (B)</p> Signup and view all the answers

What does the first law of thermodynamics state about the change in internal energy of a system?

<p>It depends on heat added and work done by the system. (D)</p> Signup and view all the answers

In which type of thermodynamic process does no heat transfer occur?

<p>Adiabatic process (C)</p> Signup and view all the answers

Which equation correctly relates the molar heat capacities of an ideal gas?

<p>Cp = CV + R (A)</p> Signup and view all the answers

For an ideal gas undergoing an adiabatic process, which statement is true?

<p>The product of temperature and volume raised to the power of γ-1 is constant. (D)</p> Signup and view all the answers

What characterizes a reversible thermodynamic process?

<p>It can be reversed by an infinitesimal change in conditions. (A)</p> Signup and view all the answers

Which of the following statements about internal energy is true for an ideal gas?

<p>It depends only on temperature. (B)</p> Signup and view all the answers

In an isochoric process, what remains constant?

<p>Volume (A)</p> Signup and view all the answers

Which of these expressions is NOT correct for work done during an adiabatic expansion?

<p>W = (p1V1 - p2V2)(γ - 1) (B)</p> Signup and view all the answers

What does the thermal efficiency e of a heat engine represent?

<p>The ratio of the work done to the heat absorbed from the source (C)</p> Signup and view all the answers

Which formula correctly describes the maximum thermal efficiency e of a gasoline engine operating on the Otto cycle?

<p>e = 1 - rac{1}{r^{ rac{1}{eta}}} (B)</p> Signup and view all the answers

What does the coefficient of performance K of a refrigerator indicate?

<p>The ratio of heat removed from the cold reservoir to the work input (B)</p> Signup and view all the answers

Which statement is a form of the second law of thermodynamics?

<p>Cyclic processes cannot completely convert heat into work. (C)</p> Signup and view all the answers

How does the thermal efficiency of a Carnot engine depend on the temperatures TH and TC?

<p>eCarnot = 1 - rac{TC}{TH} (C)</p> Signup and view all the answers

What happens when a Carnot engine operates in reverse?

<p>It becomes a Carnot refrigerator. (C)</p> Signup and view all the answers

What kind of processes does the Carnot cycle utilize?

<p>Reversible processes only (A)</p> Signup and view all the answers

What defines the effectiveness of a refrigerator according to its operation?

<p>The ratio of heat absorbed from a cold reservoir to the work input (B)</p> Signup and view all the answers

What does the mean free path λ depend on in an ideal gas?

<p>Number of molecules per volume and molecular radius (D)</p> Signup and view all the answers

For an ideal diatomic gas, what is the molar heat capacity at constant volume CV?

<p>$\frac{5R}{2}$ (B)</p> Signup and view all the answers

In the context of the Maxwell Boltzmann distribution, what does the function f(v) represent?

<p>Fraction of molecules with speeds between v and v + dv (C)</p> Signup and view all the answers

When work is done on a thermodynamic system, how is the work W represented?

<p>W &lt; 0 (B)</p> Signup and view all the answers

What equation represents the work done by a system when pressure is constant?

<p>W = p(V2 - V1) (C)</p> Signup and view all the answers

Which condition applies to the heat added to the system and the work done by the system?

<p>They depend on the path taken between states (C)</p> Signup and view all the answers

What is the expression for the mean free path λ in terms of the molecular radius r and number density N/V?

<p>$\lambda = \frac{v t_{mean}}{4\pi^2 r^2 N}$ (A)</p> Signup and view all the answers

How does the molar heat capacity of an ideal monatomic solid compare to that of an ideal monatomic gas?

<p>It is more than that of a monatomic gas (A)</p> Signup and view all the answers

What is the relationship between the temperatures and the corresponding gas-thermometer pressures of two gases at thermal equilibrium?

<p>The temperatures are equal and pressures are proportional. (D)</p> Signup and view all the answers

In the equation $H = \frac{dQ}{dt} = kA \frac{(T_H - T_C)}{L}$, what does H represent?

<p>The rate of heat transfer. (B)</p> Signup and view all the answers

What does the coefficient of volume expansion, β, for a solid relate to?

<p>It is three times the value of α. (D)</p> Signup and view all the answers

Which mode of heat transfer does NOT involve bulk motion of materials?

<p>Conduction. (D)</p> Signup and view all the answers

What is the formula for the change in linear dimension due to temperature change?

<p>∆L = αL0∆T. (C)</p> Signup and view all the answers

During convection, heat is transferred through:

<p>Mass motion of fluids. (A)</p> Signup and view all the answers

What condition is necessary for two bodies to achieve thermal equilibrium?

<p>They must be at the same temperature. (D)</p> Signup and view all the answers

What does the emissivity of a surface affect in terms of radiation heat transfer?

<p>The efficiency of energy transfer through radiation. (D)</p> Signup and view all the answers

Flashcards

Entropy

A measure of the randomness or disorder within a system.

Entropy Change in Reversible Processes

The change in entropy during a reversible process is calculated by dividing the heat flow by the absolute temperature.

Carnot Refrigerator Efficiency

No refrigerator can have a higher coefficient of performance than a Carnot refrigerator operating between the same temperatures.

Entropy and Isolated Systems

The total entropy of an isolated system can only increase or stay the same. It cannot decrease.

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Entropy and Interactions

When a system interacts with its surroundings, the total entropy change of the system and surroundings cannot decrease. It either stays the same or increases.

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Thermal efficiency (e)

A measure of how efficiently a heat engine converts absorbed heat into work.

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Otto cycle

A type of engine that works in a closed loop with four stages: intake, compression, power, and exhaust.

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Compression ratio (r)

The ratio of the volume of the cylinder at the end of the intake stroke to the volume at the end of the compression stroke.

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Refrigerator

A device that transfers heat from a colder place to a warmer place using work input.

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Coefficient of performance (K)

A measure of the effectiveness of a refrigerator, which is the ratio of the heat removed from the cold reservoir to the work input.

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Second law of thermodynamics

A fundamental principle of thermodynamics that states that natural processes tend to proceed in a direction that increases entropy.

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Carnot cycle

A theoretical thermodynamic cycle that operates between two heat reservoirs at different temperatures and uses only reversible processes.

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Carnot efficiency (eCarnot)

The maximum efficiency of a heat engine operating between two specific temperatures.

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Thermal Equilibrium

Two objects in thermal equilibrium have the same temperature. A conducting material allows heat to flow between objects, reaching thermal equilibrium. An insulating material resists heat flow.

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Kelvin Scale

A temperature scale where 0 Kelvin is the extrapolated zero-pressure temperature of a gas thermometer. It's related to Celsius by: TK = TC + 273.15

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Gas-thermometer scale

The ratio of two temperatures on the gas-thermometer scale is equal to the ratio of the corresponding gas-thermometer pressures: T2/T1 = p2/p1

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Linear Thermal Expansion

A temperature change ∆T causes a change in a solid's length L0. The change ∆L is proportional to L0 and ∆T: ∆L = αL0 ∆T

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Volume Thermal Expansion

A temperature change ∆T causes a change in the volume V0 of a solid or liquid. The change ∆V is proportional to V0 and ∆T: ∆V = βV0 ∆T

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Conduction

Heat transfer within a material without bulk motion. The heat current H depends on the area A, length L, temperature difference (TH − TC ), and thermal conductivity k: H = (kA(TH − TC))/L

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Convection

Heat transfer involving mass motion. Think of air currents transferring heat from a stove to a room.

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Radiation

Heat transfer through electromagnetic radiation. The radiation heat current H depends on the surface area A, emissivity of the surface (0 - 1), and temperature T: H = AσT4

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First law of thermodynamics

The change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

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Adiabatic process

A process where no heat enters or leaves the system.

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Isochoric process

A process that happens at a constant volume.

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Isobaric process

A process that happens at a constant pressure.

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Isothermal process

A process that happens at a constant temperature.

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Internal energy of an ideal gas

The internal energy of an ideal gas depends only on its temperature.

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Molar heat capacities of an ideal gas

The molar heat capacity at constant pressure is greater than the molar heat capacity at constant volume by the ideal gas constant.

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Reversible process

A reversible process is one that can be reversed by an infinitesimal change in conditions.

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Net Radiation Heat Current (Hnet)

The net radiation heat current (Hnet) is determined by the difference in temperature raised to the fourth power between a body (T) and its surroundings (Ts). It's calculated as Hnet = A σ(T⁴ − Ts⁴), where A is the surface area, and σ is the Stefan-Boltzmann constant.

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Equation of State

An equation of state describes the relationship between pressure (p), volume (V), and absolute temperature (T) of a given amount of substance. This relationship only applies in equilibrium states where these properties are uniform throughout the system. The ideal-gas equation of state is a common example, expressed as pV = nRT, where n is the number of moles, and R is the ideal gas constant.

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Molar Mass (M)

The molar mass (M) of a pure substance is the mass per mole. It's calculated as M = NA m, where NA is Avogadro's number (the number of molecules in a mole) and m is the mass of one molecule.

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Total Translational Kinetic Energy of an Ideal Gas

The total translational kinetic energy of the molecules in a gas is directly proportional to the absolute temperature (T). This is expressed as Ktr = (3/2) nRT, where n is the number of moles, and R is the ideal gas constant.

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Root-Mean-Square (RMS) Speed

The root-mean-square speed (vrms) of molecules in an ideal gas is calculated as vrms = √(3kT/m), where k is the Boltzmann constant, T is the absolute temperature, and m is the mass of a molecule.

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Mean Free Path (λ)

The average distance a molecule travels before colliding with another molecule. It depends on the density (N/V) of the gas and the size of the molecules (represented by the molecular radius r).

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Molar Heat Capacity (CV)

The amount of energy required to raise the temperature of one mole of a substance by one degree Celsius (or Kelvin).

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Molar Heat Capacity (CV) of a monatomic gas

For an ideal monatomic gas, it's 3/2 times the gas constant (R). This represents the energy needed to raise the temperature by exciting its three translational degrees of freedom.

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Molar Heat Capacity (CV) of a diatomic gas

For an ideal diatomic gas, it's 5/2 times the gas constant (R). This means the energy is needed for translation and rotation.

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Molar Heat Capacity (CV) of a monatomic solid

For an ideal monatomic solid, it's 3 times the gas constant (R). This represents the energy needed to excite vibrations in a solid, where each atom has three vibrational degrees of freedom.

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Maxwell-Boltzmann Distribution (f(v))

Describes the distribution of speeds of molecules in an ideal gas. It shows that the fraction of molecules with a given speed is related to their mass, temperature, and the speed itself.

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Heat (Q)

The amount of energy transferred to a system by thermal means. This represents the energy related to the random motion of the molecules in a system.

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Work (W)

The amount of energy transferred to a system by mechanical work. This involves forces acting over a distance and involves organized motion of the system.

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Study Notes

Temperature and Heat

  • Two bodies in thermal equilibrium have the same temperature. A conducting material allows interaction and equilibrium, while an insulator prevents it.
  • If systems A and B are each in thermal equilibrium with system C, then A and B are in thermal equilibrium with each other.
  • The Kelvin scale's zero point is extrapolated from a gas thermometer's zero-pressure temperature (-273.15°C = 0 K).
  • Temperature ratio (T₂/T₁) equals pressure ratio (p₂/p₁) in a gas thermometer.

Thermal Expansion

  • A temperature change (ΔT) causes a change in any linear dimension (ΔL) of a solid.
  • ΔL is proportional to the original length (L₀) and ΔT.
  • Similarly, a temperature change causes a volume change (ΔV) in a solid or liquid. ΔV is proportional to the original volume (V₀) and ΔT.
  • The coefficients (α and β) represent linear and volume expansion, respectively. For solids, β = 3α.

Conduction, Convection, and Radiation

  • Conduction is heat transfer within a material without bulk motion.
  • Heat current (H) depends on area (A), length (L), temperature difference (TH - TC), and thermal conductivity (k) of the material.
  • H = kA(TH - TC)/L

Equations of State of Matter

  • Pressure (P), volume (V), and absolute temperature (T) of a substance are related by an equation of state.
  • For an ideal gas, PV = nRT (where n is the number of moles and R is the ideal gas constant).

Molecular Properties of Matter

  • Molar mass (M) is mass per mole of a substance.
  • Total mass (mtotal) = number of moles (n) x molar mass (M).
  • Avogadro's number (NA) is the number of molecules per mole.
  • Mass of a single molecule (m) = Molar mass (M) / Avogadro's number (NA)

Kinetic-Molecular Model of an Ideal Gas

  • Total translational kinetic energy (Ktr) of an ideal gas is given as: Ktr = 3nRT/2.
  • Average translational kinetic energy per molecule (1/2 m(v²)av).
  • Root mean square speed (vrms) of molecules: vrms = √(3kT/m) where k is the Boltzmann constant.

Heat Capacities

  • Molar heat capacity at constant volume (Cv) is a multiple of the gas constant (R) for certain idealized cases.
    • Ideal monatomic gas: Cv = 3R/2.
    • Ideal diatomic gas with rotational energy: Cv = 5R/2.
    • Ideal monatomic solid: Cv = 3R

Molecular Speeds

  • Molecular speeds in an ideal gas follow the Maxwell-Boltzmann distribution f(v).
  • f(v) dv describes the fraction of molecules with speeds between v and v + dv.

The First Law of Thermodynamics

  • A thermodynamic system exchanges energy with its surroundings via heat transfer or work.
  • Work done by a system changing volume from V₁ to V₂ at pressure P is: W = ∫V1V2 PdV
  • If pressure is constant, W = p(V₂ - V₁).
  • ∆U = Q - W. (Change in internal energy is equal to heat added minus work done)

The First Law of Thermodynamics, Important Kinds of Thermodynamic Processes

  • Adiabatic process: no heat transfer (Q = 0).
  • Isochoric process: constant volume (W = 0).
  • Isobaric process: constant pressure.
  • Isothermal process: constant temperature.

Thermodynamics of Ideal Gases

  • Internal energy (U) of an ideal gas depends only on temperature.
  • Molar heat capacities (Cv and Cp) for ideal gases differ by the ideal gas constant (R).
  • Cp = Cv + R
  • The dimensionless ratio of heat capacities (Cp/Cv) is denoted by γ.

Adiabatic Processes in Ideal Gases

  • For an adiabatic process in an ideal gas, TVγ-1 and pVγ are constant.
  • Work done during an adiabatic process involves initial and final values of temperature or pressure and volume.

The Second Law of Thermodynamics

  • Reversible process: direction can be reversed by infinitesimal change in conditions.
  • All other processes are irreversible
  • Total entropy change of system and surroundings can never decrease.

Heat Engines

  • A heat engine takes heat (QH) from a high-temperature source, converts some to work (W), and releases the rest (Qc) to a low-temperature sink.
  • Efficiency (e) = W/QH = 1 - (Qc/QH).
  • The Otto cycle is a theoretical model for a gasoline engine.
  • Efficiency depends on the compression ratio and the heat capacity ratio (γ).

Refrigerators

  • A refrigerator takes heat (Qc) from a cold place, uses work (|W|) and releases heat (|QH|) to a warm place.
  • Coefficient of performance (K) = Qc/|W|.
  • Carnot refrigerator has the highest coefficient of performance for given temperatures.

Entropy

  • Entropy measures the randomness of a system.
  • For a reversible process: ∆S=∫(dQ/T).
  • Entropy depends only on the initial and final states of the system.
  • The total entropy of an isolated system never decreases.

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Description

Explore the fundamental concepts of temperature, heat, and thermal properties in this quiz. Understand the laws of thermal equilibrium, thermal expansion, and the mechanisms of heat transfer such as conduction, convection, and radiation. Test your knowledge and deepen your understanding of this essential topic in physics.

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