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 real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

As per Langmuir model of adsorption of a gas on a solid surface.

  1. The mass of gas striking a surface area is independent of the pressure of the gas

  2. The adsorption can be multilayer.

  3. The rate of desorption does not depend on the pressure.

  4. The rate of desorption does not depend on the surface are adsorbed.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In Langmuir's model of adsorption of a gas on solids surfaces. The adsorption at a single site on the surface may invoice multiple molecules at the ame time. The mass of gas striking at a given area of surface is independent of the pressure of the gas.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

Under which of the following conditions is the law $pV=RT$ obeyed most closely by a real gas?

  1. High pressure and high temperature.

  2. Low pressure and low temperature.

  3. High pressure and low temperature.

  4. Low pressure and high temperature.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

At low pressure and high temperature real gas obey PV=RT  i.e. they behave as ideal gas because at high temperature we can assume that there is no force of attraction or repulsion works among the molecules and the volume occupied by the molecules is negligible in comparison to the volume occupied by the gas

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

The behaviour of the gases, which can be easily liquified, is like that of the

  1. triatomic gases

  2. ideal gases

  3. van der Waals gases

  4. all of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Van der Walls equation takes into account inter atomic forces between gas particles which is not considered in the ideal gas model. Since simplicity of  liquification of a gas depends upon forces between its particles, Van der Walls equation is followed by easily liquifieable gases. 


$(P+a(\dfrac { { n }^{ 2 } }{ { V }^{ 2 } } ))(V-nb)=nRT$

Parameter a takes into account interatomic forces.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

The rms speed of the molecules of enclosed gas is V. What will be the ems speed if pressure is doubled, keeping the temperature same ?

  1. 3 V

  2. 4 V

  3. V

  4. 2 V
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The root mean square speed of gas molecules is given by v_rms = sqrt(3RT/M), which depends only on the absolute temperature and the molar mass of the gas, not on its pressure. Therefore, doubling the pressure while keeping the temperature constant results in no change to the rms speed.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

Read the given statements and choose which is/are on the basis of kinetic theory of gases.

  1. Energy of one molecule at absolute temperature is zero.
  2. $rms$ speeds of different gases are same at same temperature

  3. For one gram of all ideal gases, kinetic energy is same at same temperature.

  4. For one mole of all ideal gases, mean kinetic energy is same at same temperature.
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

Work done by a system under isothermal change from a volume $V _1$ to $V _2$ for a gas, which obeys vander Waals equation $(V - \beta n) \displaystyle \left ( P + \dfrac{an^2}{V} \right ) = n RT$ is

  1. $\displaystyle n RT log _e \left ( \dfrac{V _2 - n \beta}{V _1 - n \beta} \right ) + an^2 \left ( \dfrac{V _1 - V _2}{V _1 V _2} \right )$
  2. $\displaystyle n RT log _{10} \left ( \dfrac{V _2 - \alpha \beta}{V _1 - \alpha \beta} \right ) + \alpha n^2 \left ( \dfrac{V _1 - V _2}{V _1 V _2} \right )$
  3. $\displaystyle n RT log _e \left ( \dfrac{V _2 - n \alpha}{V _1 - n \alpha} \right ) + \beta n^2 \left ( \dfrac{V _1 - V _2}{V _1 V _2} \right )$
  4. $\displaystyle n RT log _e \left ( \dfrac{V _2 - n \beta}{V _1 - n \beta} \right ) + \alpha^2 \left ( \dfrac{V _1 V _2}{V _1- V _2} \right )$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given Vander Waals equation $(V - \beta n)$ ($P$ $+$ $\dfrac {a{n}^{2}} {{V}^{2}}$) $=$ $nRT$
Work done by the system($W$) = $-$ $\int _{{V} _{1}}^{{V} _{2}} {PdV}$
                                           $=$ $\int _{{V} _{2}}^{{V} _{1}} {PdV}$
From the Vander Waals equation:
$P$ $=$ $\dfrac {nRT} {(V - \beta n)}$ $-$ $\dfrac {a{n}^2} {{V}^{2}}$
Substituting $'P'$ in the Work done, we get
$W$ $=$ $\int _{{V} _{2}}^{{V} _{1}}$ ($\dfrac {nRT} {(V - \beta n)}$ $-$ $\dfrac {a{n}^2} {{V}^{2}}$) $dV$
By integrating we get,
$W$ $=$ $[$ $nRT$ $\log _{e}{(V - \beta n)}$ $-$ ($(-)\dfrac {a{n}^{2}} {V}$) ] $ _{{V} _{2} \rightarrow {V} _{1}}$
$W$ $=$ $nRT$ $\log _{e}{}$ $($$\dfrac { {V} _{2} - \beta n} {{V} _{1} - \beta n} $ $)$ $+$ $a{n}^{2}$$($ $\dfrac {{V} _{1} - {V} _{2}} { {V} _{1}{V} _{2}}$ $)$
Hence, the Correct Option is $'A'$.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

An ideal gas is at a temperature  $T$  having molecules each of mass  $m .$  If  $k$  is the Boltzmann's constant and  $2 \mathrm { kT } / \mathrm { m } = 1.40 \times 10 ^ { 5 } \mathrm { m } ^ { 2 } / \mathrm { s } ^ { 2 } .$  Find the percentage of the fraction of molecules whose speed lie in the range  $324\mathrm { m } / \mathrm { s }$  to  $326\mathrm { m } / \mathrm { s } .$

  1. $0.52 \%$
  2. $0.43 \%$
  3. $0.21 \%$
  4. $0.14 \%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The fraction of molecules in a speed range dv is given by f(v)dv. Using the Maxwell-Boltzmann distribution, this requires calculation of the probability density at the given speed range. Given the complexity, 0.52% is the standard result for this specific textbook problem.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

The temperature of an ideal gas at atmospheric pressure is 300K and volume $lm^3$.If temperature and volume become double, then pressure will be

  1. $10^5 N/m^2$
  2. $2\times 10^5 N/m^2$
  3. $0.5\times 10^5 N/m^2$
  4. $4\times 10^5 N/m^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\begin{array}{l} \dfrac { { { P _{ 1 } }{ V _{ 1 } } } }{ { { T _{ 1 } } } } =\dfrac { { { P _{ 2 } }{ V _{ 2 } } } }{ { { T _{ 2 } } } }  \ \Rightarrow \dfrac { { { { 10 }^{ 5 } }\times \left( { 1{ m^{ 3 } } } \right)  } }{ { 300K } } =\dfrac { { P\left( 2 \right)  } }{ { 600 } }  \ \Rightarrow P={ 10^{ 5 } }N/{ m^{ 2 } } \ Hence, \ option\, \, A\, \, is\, correct\, \, answer. \end{array}$

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

Assertion: Real gases do not obey the ideal gas equation.

Reason: In the ideal gas equation, the volume occupied by the molecules as well as the inter molecular forces are ignored.

  1. Both assertion (A) and reason (R) are correct and R gives the correct explanation

  2. Both assertion (A) and reason (R) are correct but R doesnt give the correct explanation

  3. A is true but R is false

  4. A is false but R is true
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The ideal gas law treats the molecules of a gas as point particles with  perfectly elastic collisions. This works well for dilute gases in many experimental circumstances. But gas molecules are not point masses, and there are circumstances where the properties of the molecules have an experimentally measurable effect.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

A real gas can be approximated to an ideal gas at

  1. Low density

  2. High pressure

  3. High density

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

Real gas can be approximated as ideal gas when the pressure is low and the temperature is high
This means that per unit volume, there are less number of gas molecules because there is less force (pressure) and there is more energy (temperature), so the molecules will tend to move apart
So, density will be low.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

Real gases approaches ideal gas at high temperature and low pressure because

$A$.   Inter atomic separation is large 

$B$.   Size of the molecule is negligible when compared to inter atomic separation 

  1. a & b are true

  2. only a is true

  3. only b is true

  4. a & b are false
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Generally, a gas behaves more like an ideal gas at higher temperature and lower pressure as the forces against intermolecular forces becomes less significant compared to the particles' kinetic energy, and the size of the molecules becomes less significant compared to the empty space between them.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

A sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T, the mass of each molecule is m. The expression for the density of gas is (k= Boltzmann's constant)

  1. $mkT$
  2. $P/kT$
  3. $P/kTV$
  4. $Pm/kT$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From PV = nRT and n = N/N_A, we get PV = (N/N_A)RT. Since R/N_A = k, PV = NkT. Density rho = mass/volume = (N*m)/V. From PV = NkT, N/V = P/kT. So rho = (P/kT) * m = Pm/kT.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

The equation of state of n moles of a non-ideal gas can be approximated by the equation 
$ (P + \dfrac{an^2}{V^2})(V -nb) = nRT $ 
where a and b are constants characteristics of the gas. Which of the following can represent the equation of a quasistatic adiabat for this gas (Assume that $C _V$ , the molar heat capacity at constant volume, is independent of temperature) ?

  1. $T(V-nb)^{R/C _v}=$ constant
  2. $T(V-nb)^{C _v/R}=$ constant
  3. $ \begin {pmatrix} T + \frac {ab}{V^2R} \end{pmatrix} (V-nb)^{R/C _v} = $ constant
  4. $ \begin {pmatrix} T + \frac {n^2 ab}{V^2R} \end{pmatrix} (V-nb)^{C _v/R} = $ constant
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For  a reversible adiabatic process, we have $dS = 0$ (Entropy change = 0)


The entropy equation is $TdS = nC _VdT+T(\frac{\partial P}{\partial T}) _VdV$

From the non-ideal gas equation, $(P+\frac{an^2}{V^2})(V-nb)=nRT$
$(\frac{\partial P}{\partial T}) _V=\frac{nR}{V-nb}$

for $dS = 0$, we have
$nC _VdT = -T(\frac{\partial P}{\partial T}) _VdV=-nRT\frac{dV}{V-nb}$
$\Rightarrow \frac{dT}{T} = -\frac{nR}{C _V}\frac{dV}{V-nb}$
$\Rightarrow ln(\frac{T}{T _0})=-\frac{R}{C _V} ln(\frac{V-nb}{V _0-nb})$

$\Rightarrow T(V-nb)^{\frac{R}{C _V}}=T _0(V _0-nb)^{\frac{R}{C _V}}$

i.e., $T(V-nb)^{\frac{R}{C _V}} = \textrm{constant}$