Physics (PHYS201) Midterm Sample

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Questions and Answers

Explain how an isothermal process affects the internal energy of an ideal gas.

In an isothermal process, the temperature of the gas remains constant. For an ideal gas, internal energy depends only on temperature, so the internal energy does not change.

Describe what happens to the water level when an ice cube melts in a cup filled to the brim with water.

The water level remains the same.

Briefly explain the concept of multiplicity in statistical mechanics.

Multiplicity refers to the number of microstates that correspond to the same macrostate of a system. It quantifies the number of ways a system can arrange its components to achieve the same overall properties.

What is the relationship between entropy and the number of microstates in a system?

<p>Entropy is proportional to the logarithm of the number of microstates. This relationship is mathematically expressed as $S = k_B \ln{\Omega}$, where $S$ is the entropy, $k_B$ is the Boltzmann constant, and $\Omega$ is the number of microstates.</p>
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Describe how the heat capacity of a substance typically behaves as the temperature approaches absolute zero.

<p>As the temperature approaches absolute zero, the heat capacity of a substance tends to decrease and approach zero. This is due to the reduction in available energy levels for particles to occupy, making it more difficult to increase the system's energy.</p>
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Explain the difference between an isothermal and an adiabatic process. How do they differ in terms of heat transfer and temperature change?

<p>In an isothermal process, the temperature remains constant, and heat is transferred to maintain this constant temperature. In an adiabatic process, there is no heat transfer between the system and its surroundings, and the temperature changes as work is done.</p>
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What is the significance of the adiabatic index ($\gamma$) in thermodynamics, and how does it relate to the properties of a gas?

<p>The adiabatic index ($\gamma$) is the ratio of the heat capacity at constant pressure ($C_p$) to the heat capacity at constant volume ($C_v$), i.e., $\gamma = \frac{C_p}{C_v}$. It characterizes how the temperature of a gas changes during an adiabatic process. For monatomic gases, $\gamma$ is approximately 1.67, while for diatomic gases, it is approximately 1.4.</p>
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Explain what limits the efficiency of a Carnot engine.

<p>The efficiency of a Carnot engine is limited by the temperatures of the hot and cold reservoirs between which it operates. It is given by $\eta = 1 - \frac{T_c}{T_h}$, where $T_c$ is the absolute temperature of the cold reservoir and $T_h$ is the absolute temperature of the hot reservoir. The larger the temperature difference, the higher the efficiency.</p>
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How does the specific heat capacity of a substance affect its temperature change when heat is added?

<p>Specific heat capacity is defined as the amount of heat required to raise the temperature of one unit mass of a substance by one degree, thus materials with higher specific heat capacity require more energy to change temperature than those with low specific heat capacity.</p>
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State Pascal's principle and describe its application in hydraulic systems.

<p>Pascal's principle states that pressure applied to a confined fluid is transmitted equally in all directions throughout the fluid. In hydraulic systems, this principle is used to multiply force: a small force applied to a small area results in a larger force on a larger area.</p>
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Explain the concept of buoyancy and the conditions necessary for an object to float in a fluid.

<p>Buoyancy is the upward force exerted by a fluid that opposes the weight of an immersed object. An object floats when the buoyant force is equal to the weight of the object, which occurs when the density of the object is less than or equal to the density of the fluid.</p>
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What's the relationship between the change in the thermal energy of a gas and the work done on/by the gas in an adiabatic process?

<p>In an adiabatic process, there is no heat exchange with the surroundings. Therefore, any change in the thermal energy of the gas is <em>equal</em> to the work done on or by the gas. If work is done ON the gas it increases the internal energy.</p>
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Explain how an increase in the number of gas molecules inside a container affects the pressure, assuming constant volume and temperature.

<p>An increase in the number of gas molecules inside a container leads to a proportional increase in pressure. This relationship is described by the ideal gas law, $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the ideal gas constant, and $T$ is temperature. If $V$ and $T$ are constant, increasing $n$ increases $P$.</p>
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In the context of statistical mechanics and entropy, explain the difference between a microstate and a macrostate.

<p>A microstate is a specific configuration of a system at a microscopic level, detailing the state of each individual particle. A macrostate, on the other hand, is a description of the system's overall, macroscopic properties such as temperature, pressure, and volume. Many different microstates can correspond to the same macrostate.</p>
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How does the density of an object affect whether it floats or sinks in a fluid?

<p>If the density of an object is less than the density of the fluid, the object will float. If the density of the object is greater than the density of the fluid, the object will sink. If the densities are equal, the object will neither sink nor float, maintaining a neutral buoyancy.</p>
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Describe how the temperature difference between the hot and cold reservoirs affects the performance of a heat engine.

<p>The greater the temperature difference between the hot and cold reservoirs, the more efficient a heat engine can be. A larger temperature difference allows the engine to convert more of the heat energy into useful work, as dictated by the Carnot efficiency formula.</p>
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In an adiabatic expansion, what happens to the temperature of an ideal gas, and why?

<p>In an adiabatic expansion, the temperature of an ideal gas decreases. This occurs because the gas does work on its surroundings as it expands, and since there is no heat transfer in an adiabatic process, this work is done at the expense of the gas's internal energy, which is directly related to its temperature.</p>
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What are the key factors determining the net force on a submerged object?

<p>The key factors determining the net force on a submerged object are the buoyant force (which depends on the volume of fluid displaced) and the object's weight. The net force is the vector sum of these two forces; its direction determines whether the object floats, sinks, or remains in equilibrium underwater.</p>
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Explain what determines the rate of heat transfer between two objects at different temperatures.

<p>The rate of heat transfer depends on the temperature difference between the objects, the thermal conductivity of the materials involved, the surface area in contact, and the distance between the objects. According to Fourier's Law, the rate of heat transfer is proportional to the temperature gradient and the area, and inversely proportional to the distance.</p>
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Describe the relationship between the first law of thermodynamics and the concepts of work, heat, and internal energy of a system.

<p>The first law of thermodynamics states that the change in internal energy ($\Delta U$) of a system is equal to the heat added to the system ($Q$) minus the work done by the system ($W$): $\Delta U = Q - W$. This law expresses the conservation of energy, indicating that energy can be transferred between a system and its surroundings in the form of heat and work, leading to a corresponding change in the system's internal energy.</p>
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Flashcards

What is Entropy?

The total disorder or randomness in a system.

What are Microstates?

The number of ways a particular macroscopic state can be realized.

What is an Adiabatic Process?

A process where no heat is transferred into or out of the system.

What is a Carnot Engine?

An ideal engine that operates in a reversible cycle between two heat reservoirs.

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What is the Adiabatic Index?

The ratio of specific heats at constant pressure and constant volume.

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What is a Hydraulic System?

A device that uses liquid to transmit force or pressure.

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What is Buoyant Force?

The upward force exerted by a fluid that opposes the weight of an immersed object.

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Study Notes

  • This is a sample midterm exam for General Physics III (PHYS201) taught by Prof. M. Leifer at Chapman University, Schmid College of Science and Technology, Spring 2025
  • The exam is to be completed within 75 minutes
  • The exam consists of two sections
    • Section 1 contains multiple-choice questions
    • Section 2 contains problems where only two out of the three questions are to be answered
  • All work must be shown in the provided booklet
  • A 2-sided page of notes is permitted, but no other books or notes
  • Calculators, computers, and electronic devices are allowed with disabled internet
  • Permitted software includes built-in calculator apps, Qalculate, MATLAB, Maple, Mathematica, and Python Notebooks
  • Any other apps must be approved by the instructor
  • Section 1 contains 4 multiple choice questions, each worth 2 points
  • Section 2 contains 3 problems, each worth 10 points
  • The total exam is worth 28 points

Entropy and the Environment

  • In any natural process, the cumulative entropy of a system alongside its surrounding environment always increases

Helium, Oxygen, and Thermal Energy

  • A container filled with helium and oxygen is in thermal equilibrium
  • Oxygen molecules are more massive than helium molecules
  • Both gas types possess the same average thermal energy

Isothermal Expansion of Ideal Gas

  • During the isothermal expansion of an ideal gas, its thermal energy remains constant

Ice Melting in Water

  • A cup is filled to the brim with water containing an ice cube at 0°C with part of the ice cube sticking out of the water's surface
  • The water level remains the same as the ice melts

Entropy Problem: Distinguishable Particles

  • A system contains three distinguishable particles with four units of energy distributed among them
  • Determine the number of microstates
  • Find the probability that at least one particle has exactly two energy units at equilibrium

Einstein Solid Multiplicity

  • The multiplicity of a large Einstein solid at low temperature = (eN/q)^q
  • The solid contains N oscillators, q units of energy, and ϵ is its energy unit size
  • Calculate the entropy in terms of N, U, ϵ, and the Boltzmann constant (kB)
  • Find an expression for the total thermal energy (U) in terms of N, ϵ, temperature (T), and kB
  • Determine the heat capacity (C) for the system and its behavior as T approaches 0

Thermodynamics of Monatomic Ideal Gas

  • An adiabatic process occurs with a fixed amount of monatomic ideal gas
  • The temperature increases from 35°C to 45°C
  • The gas contains 4.2 × 10^23 molecules
  • Calculate the change in thermal energy
  • Determine the heat transfer
  • Determine the work done by the environment
  • The adiabatic index of the gas is γ = 1.5
  • Calculate the factor by which the volume changes during this process

Carnot Engine

  • An ideal Carnot engine operates between 250°C and 10°C
  • Energy transferred from the engine to the cold reservoir heats a 50.0g iron block by 6.0°C each cycle
  • The specific heat capacity of iron is 0.45 kJ/kg·K
  • Find the heat engine's efficiency
  • Determine the energy transferred to the cold reservoir per cycle
  • Determine the work done by the environment on the heat engine each cycle

Fluids and Manometers

  • Two open water reservoirs with a water density of 1000 kg/m³
  • A manometer contains incompressible mercury with a density of 13,600 kg/m³
  • A manometer reading (m) is at 25.0 cm
  • Calculation of the difference in elevation (h)

Hydraulic Systems

  • A hydraulic system reduces the magnitude of a force using circular pistons
  • Piston A has a radius of 0.88 m, applying a downward force of 13700 N
  • Piston B has an upward force of 1020 N
  • Find the fluid pressure exerted on piston B and its radius

Submerged Object

  • A 100 kg object with a volume of 1 m³ is submerged 2 m below water
  • Determine the magnitude and direction of the net force acting on the object

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