Physics

Thermodynamics and Gas Laws

626 Questions

Thermodynamics and gas laws questions test the understanding of ideal gas behavior, work done during thermodynamic processes, and specific heat ratios. Key areas include isothermal, adiabatic, and isobaric expansions along with real gas deviations. These mathematical physics concepts are standard in engineering and general science competitive exams.

Ideal gas equationIsothermal and adiabatic processesThermodynamic workGas kinetic theoryReal gas behavior

Thermodynamics and Gas Laws Questions

Multiple choice physics behaviour of perfect gas and kinetic theory of gases degree of freedom: law of equipartition of energy law of equipartition of energy law of equipartition of energy and mean free path

The average degree of freedom per molecule for a gas is 6. The gas performs 25 J of work when it expands at constant pressure. The heat absorbed by the gas is

  1. 75 J

  2. 100 J

  3. 150 J

  4. 125 J
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Delta u=\dfrac{f}{2}RT=3RT$

$\Delta w=nR\Delta T=25.5$
$\Delta Q=\Delta V+\Delta W$
$=3nR\Delta T+nR\Delta T=4nR\Delta T$
$=4\times 25=100\ J$

Multiple choice physics behaviour of perfect gas and kinetic theory of gases degree of freedom: law of equipartition of energy law of equipartition of energy law of equipartition of energy and mean free path

A gas performs Q work when it expand at constant pressure. During this process heat absorbed by the gas is 4Q. The average number of degrees of freedom for the gas is:

  1. 5

  2. 6

  3. 4

  4. 3.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

At constant pressure, Q = n*Cp*deltaT and W = n*R*deltaT. Given Q = 4Q (this seems to be a typo in the prompt, likely Q_heat = 4*W). If Q_heat = 4*W, then Cp*deltaT = 4*R*deltaT, so Cp = 4R. Since Cp = (f/2 + 1)R, then f/2 + 1 = 4, f/2 = 3, f = 6.

Multiple choice physics behaviour of perfect gas and kinetic theory of gases degree of freedom: law of equipartition of energy law of equipartition of energy law of equipartition of energy and mean free path

N moles of an ideal diatomic gas is contained in a cylinder at temperature $T.$ On supplying some heat to cylinder, $N/3$ moles of gas disassociated into atoms while temperature remains constant. Heat supplied to the gas is

  1. $\dfrac {NRT}{3}$
  2. $\dfrac {5NRT}{2}$
  3. $\dfrac {8NRT}{3}$
  4. $\dfrac {NRT}{6}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics behaviour of perfect gas and kinetic theory of gases degree of freedom: law of equipartition of energy law of equipartition of energy law of equipartition of energy and mean free path

The heat capacity at constant volume of a sample of a monoatomic gas is $35\ J/K$. Find the number of moles.

  1. $12.81 \ \ mol $
  2. $21.81 \ \ mol $
  3. $4.81 \ \ mol $
  4. $2.81 \ \ mol $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For monoatomic gas, degrees of freedom is 3. 


Since ${ C } _{ V }=\dfrac { f }{ 2 } nR$

Hence, $35=\dfrac { 3 }{ 2 } n(8.314)$

$n=\dfrac { 70 }{ 3\times 8.314 } =2.81mol$

Answer is $2.81mol.$

Multiple choice physics behaviour of perfect gas and kinetic theory of gases degree of freedom: law of equipartition of energy law of equipartition of energy law of equipartition of energy and mean free path

Relation between pressure ($P$) and energy density ($E$) of an ideal gas is-

  1. $P=2/3E$
  2. $P=3/2E$
  3. $P=3/5E$
  4. $P=E$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Kinetic energy $=\dfrac{1}{2}{ MV } _{ rms }$
$\Rightarrow \dfrac{1}{2}M\left( \dfrac { 3RT }{ M }  \right) $        $[M=$ molar mass,$ { V } _{ rms }=\sqrt { \dfrac { 3KT }{ { m } }  } =\sqrt { \dfrac { 3RT }{ M }  } ]$
$=\dfrac{3}{2}RT$
$\Rightarrow K.E=\dfrac{3}{2}PV$          $[PV=RT]$
$\Rightarrow \dfrac{K.E}{V}=\dfrac{3}{2}P$
$\Rightarrow E=\dfrac{3P}{2}$        $E=$ Energy density.
Hence, the answer is $P=\dfrac{2}{3}E.$
Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

PRESSURE AND KINETIC INTERPRETATION OF TEMPERATURE
At what temperature the mean kinetic energy of hydrogen molecules increases to such that they will escape out of the gravitational field of earth for over?
take $({ v } _{ c }=11.2km/sec)$

  1. 12075 K

  2. 10000 K

  3. 20000 K

  4. 10075 K
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The escape velocity is related to temperature by the formula v_rms = sqrt(3RT/M). Setting v_rms equal to the escape velocity (11.2 km/s) and solving for T gives approximately 10075 K.

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

Energy associated with each molecule per degree of freedom o a system at room temperature $(27^{\circ}C)$ will be ($k$ is Boltzmann's constant)

  1. $150\;k$
  2. $(27/2)\;k$
  3. $1/2\;k$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to the equipartition theorem, the energy associated with each degree of freedom per molecule is (1/2)kT, regardless of the temperature.

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

Boltzmann's constant$ K = 1.38 \times 10^{-23} J/k $ The energy associated with helium atom the surface of sun, where surface temperature is 6000 K is

  1. $ 1.242 \times 10^{-19} J $
  2. $ 2.484 \times 10^{-19} J $
  3. $ 207 \times 10^{-19} J $
  4. $ 0.621 \times 10^{-19} J $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The average kinetic energy of a gas molecule is (3/2)kT. For a helium atom (monatomic), the energy is (3/2) * 1.38 * 10^-23 * 6000 = 1.5 * 1.38 * 6 * 10^-20 = 1.242 * 10^-19 J.

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

If in an ideal gas $r$ is radius of molecule, $P$ is pressure, $T$ is absolute temperature and $k$ is Boltzmann's constant, then mean free path $\overline { \lambda  } $ of gas molecules is given as

  1. $\dfrac { 4\pi \sqrt { 2 } PT }{ k{ r }^{ 2 } } $
  2. $\dfrac { 4\pi \sqrt { 2 } kT }{ P{ r }^{ 2 } } $
  3. $\dfrac { kP }{ 4\pi \sqrt { 2 } { r }^{ 2 }T } $
  4. $\dfrac { kT }{ 4\pi \sqrt { 2 } { r }^{ 2 }P } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The mean free path formula is lambda = kT / (sqrt(2) * pi * d^2 * P). Since the radius r = d/2, d = 2r, so d^2 = 4r^2. Substituting this gives lambda = kT / (4 * sqrt(2) * pi * r^2 * P).

Multiple choice bio-chemistry absorption by roots - the processes involved diffusion transport across membrane means of transport

Diffusion pressure is directly proportional to:

  1. Concentration of molecules diffusing

  2. Kinetic energy of diffusing molecule

  3. Concentration gradient

  4. All of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The same conditions of temperature and pressure, the molar mass is proportional to the mass density. Therefore, the rate of diffusion of different gases is inversely proportional to the square root of their mass densities.

So, the correct option is 'Concentration of molecules diffusing'.

Multiple choice

What is the Hamaker constant?

  1. A constant that describes the strength of van der Waals forces

  2. A constant that describes the strength of electrostatic forces

  3. A constant that describes the strength of steric forces

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Hamaker constant is a constant that describes the strength of van der Waals forces.

Multiple choice

The principle that describes the relationship between pressure, volume, and temperature of a gas is:

  1. Pascal's Law

  2. Bernoulli's Principle

  3. Boyle's Law

  4. Archimedes' Principle
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Boyle's Law states that the pressure of a gas is inversely proportional to its volume at constant temperature.

Multiple choice

The ideal gas law states that the pressure, volume, and temperature of a gas are:

  1. Directly proportional to each other

  2. Inversely proportional to each other

  3. Independent of each other
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The ideal gas law, also known as the general gas equation, states that the pressure, volume, and temperature of a gas are directly proportional to each other. This means that if one of these variables changes, the other two will also change in a proportional manner.

Multiple choice

The van der Waals equation of state takes into account:

  1. Intermolecular forces

  2. Ideal gas behavior

  3. Non-ideal gas behavior

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The van der Waals equation of state takes into account intermolecular forces, ideal gas behavior, and non-ideal gas behavior.

Multiple choice

In which field is topology used to study the behavior of fluids and gases?

  1. Fluid Dynamics

  2. Solid Mechanics

  3. Thermodynamics

  4. Electromagnetism
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Topology is used in fluid dynamics to study the behavior of fluids and gases, including their flow patterns, turbulence, and interactions with solid objects.