Physics

Thermodynamics and Gas Laws

616 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 isothermal and adiabatic processes work done by an ideal gas in isothermal expansion thermodynamic processes heat and thermodynamics

A vertical cyclinder with heat - conducting with heat conducting walls is closed at the bottom and its fitted with a smooth light piston. It contains one mole of an ideal gas. The temperature of the gas is always equal to the surrounding's temperature $T _o$ . The piston is moved up slowly to increase the volume of the gas to $n$ times. Which of the following is incorrect?

  1. Work done by the gas in $RT _o\ln (n)$.
  2. Work done against the atmosphere is $RT _o(n-1).$

  3. There is no change in the internal energy of the gas.
  4. The final presure of the gas is $\dfrac{1}{n-1}$ times its initial pressure.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work Done by gas (isothermal process) : 

$W=nRT\ln(\dfrac { { V } _{ 2 } }{ { V } _{ 1 } } )=R{ T } _{ o }\ln(n)$
Work Done against Atmosphere (Pressure of atmosphere is constant P & Volume is decreased): 

$W=P\triangle V\quad =P(nV-V)=PV(n-1)=R{ T } _{ o }(n-1)$

As there is no change in temperature hence no change is Internal Energy (Always in synchronization with atmosphere).
 Ideal Gas Equation:
$PV=nRT\ PV=R{ T } _{ o }\ P'(nV)=R{ T } _{ o }\ P'=\dfrac{P}{n}$

Multiple choice physics isothermal and adiabatic processes work done by an ideal gas in isothermal expansion thermodynamic processes heat and thermodynamics

Two moles of a gas is expanded to double its volume by two different processors. One is isobaric and the other is isothermal. If ${w} _{1}$ and ${w} _{2}$ are the works done respectively, then

  1. ${ w } _{ 2 }=\cfrac { { w } _{ 1 } }{ \ln { 2 } } $
  2. ${ w } _{ 2 }={ w } _{ 1 }$
  3. ${ w } _{ 2 }={ w } _{ 1 }\ln { 2 } $
  4. ${ w } _{ 1 }^{ 2 }={ w } _{ 2 }\ln { 2 } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume is changed from  $V _1 = V _o$  to  $V _2 = 2V _o$.
Temperature and pressure of gas at $V _o$ are  $T _o$ and $P _o$ respectively.
Thus, from ideal gas equation   $P _o V _o =nRT _o$           .....(1)
Work done in isobaric process  $w _1 = P _o (V _2-V _1) = P _o (2V _o - V _o) = P _o V _o$       .....(2)
Work done in isothermal process  $w _2 = nRT _o \ln\dfrac{V _2}{V _1}$
$\therefore$   $w _2 = nRT _o \ln \dfrac{2V _o }{V _o} = nRT _o \ln 2$
Or   $w _2 = P _oV _o \ln 2$   (from 1)
$\implies \ w _2 = w _1\ln 2$  

Multiple choice physics the kinetic model of matter force and kinetic theory change of states phase change

At what temperature rms speed of air molecules is doubled of that at NTP?

  1. $819^oC$
  2. $719^oC$
  3. $909^oC$

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

$v _{rms}\propto \sqrt{T}$
$\Rightarrow \displaystyle\frac{v^2 _1}{v^2 _2}=\frac{T _1}{T _2}$
$\Rightarrow \displaystyle\frac{v^2}{4v^2}=\frac{273}{T _2}$
$\Rightarrow \displaystyle T _2=1092K$
$=819^oC$

Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

Newton's formula for the velocity of sound in gas is

  1. $\displaystyle v= \sqrt {\frac {P}{\rho}}$
  2. $\displaystyle v= \frac {2}{3}\sqrt {\frac {P}{\rho}}$
  3. $\displaystyle v= \sqrt {\frac {\rho}{P}}$
  4. $\displaystyle v= \sqrt {\frac {2P}{\rho}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Newton's formula for velocity of sound in gas is:

$\displaystyle v= \sqrt {\frac {P}{\rho}}$, where $P$ is pressure & $\rho$ is density of gas

Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

Two monatomic ideal gases 1 and 2 of molecular masses  m$ _{1}$  and  m$ _{2}$  respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to gas 2 is given by

  1. $\dfrac{m _{1}}{m _{2}}$
  2. $\sqrt{\dfrac{m _{1}}{m _{2}}}$
  3. $\dfrac{m _{2}}{m _{1}}$
  4. $\sqrt{\dfrac{m _{2}}{m _{1}}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$\vartheta =\sqrt{\dfrac{\gamma RT}{M _{0}}}$

$So, \dfrac{\vartheta _{1}}{\vartheta _{2}}=\sqrt{\dfrac{\gamma RT}{M _{01}}}\times \sqrt{\dfrac{M _{02}}{\gamma RT}}$$=\sqrt{\dfrac{M _{02}}{M _{01}}}$$=\sqrt{\dfrac{m _{2}}{m _{1}}}$
Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

Velocity of sound in a gas proportional to

  1. square root of isothermal elasticity

  2. isothermal elasticity

  3. square root of adiabatic elasticity

  4. adiabatic elasticity
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to the Laplace's formula for velocity of sound in gases,


$v = \sqrt {\dfrac{E}{\rho}}$

where, $E = \gamma p$ is the adiabatic elasticity and $\rho$ is the  density of gas.


This is because the compression and rarefaction occurs rapidly one after  another without exchanging the thermal energy with surrounding hence, this  the process becomes adiabatic and not the isothermal. Hence, velocity of sound in a gas proportional to square root of adiabatic elasticity

Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

Two gases with different densities and same ratio of specific heats $(\gamma)$ are mixed in proportions $V _1$ and $V _2$ by volume. The velocity $C$ of sound in mixture will be given by $(C _1, \space C _2$ are velocities in individual gases$)$

  1. $\displaystyle\frac{C _1+C _2}{2}$
  2. $\sqrt{C _1C _2}$
  3. $\displaystyle\frac{C _1C _2\sqrt{(V _1+V _2)}}{\sqrt{(V _1C _2^2+V _2C _1^2)}}$
  4. $\displaystyle\frac{C _1C _2\sqrt{(V _1+V-2)}}{\sqrt{(V _1C _1^2+V _2C _2^2)}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$C _1=\sqrt{\dfrac{\gamma P}{\rho _1}}$ and $C _2=\sqrt{\dfrac{\gamma P}{\rho _2}}$

$\rho _1=\dfrac{\gamma P}{{C _1}^2}$

$\rho _2=\dfrac{\gamma P}{{C _2}^2}$
Mixture density, 
$\rho=\dfrac{\rho _1 \times V _1 + \rho _2 \times V _2}{V _1 + V _2}$

$\rho=\dfrac{\dfrac{\gamma P}{{C _1}^2} \times V _1 + \dfrac{\gamma P}{{C _2}^2} \times V _2}{V _1 + V _2}$

$\rho={\gamma P} \dfrac{\dfrac{1}{{C _1}^2} \times V _1 + \dfrac{1}{{C _2}^2} \times V _2}{V _1 + V _2}$

$C=\sqrt{\dfrac{\gamma P}{\rho}} = \sqrt{\dfrac{1}{\dfrac{\dfrac{1}{{C _1}^2} \times V _1 + \dfrac{1}{{C _2}^2} \times V _2}{V _1 + V _2}}}$

$C = C _1 C _2 \sqrt{\dfrac{V _1+V _2}{V _1 C _2^2+V _2 C _1^2}}$
Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

Standing waves of frequency 5.0 KHz are produced in a tube filled with oxygen at 300 K. The separation between the consecutive nodes is 3.3 cm. Calculate the specific heat capacities ${ C } _{ p }$   and ${ C } _{ v }$ of the gas.

  1. $20.7J/molK,29.0J/molK$
  2. $29.0J/molK,20.7J/molK$
  3. $2.90J/molK,2.07J/molK$

  4. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Distance between nodes is lambda/2 = 3.3 cm, so lambda = 6.6 cm = 0.066 m. Frequency f = 5000 Hz. Speed v = f * lambda = 5000 * 0.066 = 330 m/s. For oxygen (diatomic), v = sqrt(gamma * R * T / M). Gamma = v^2 * M / (R * T) = 330^2 * 0.032 / (8.314 * 300) = 1.4. Cp = (gamma * R) / (gamma - 1) = 1.4 * 8.314 / 0.4 = 29.1 J/molK. Cv = Cp - R = 29.1 - 8.314 = 20.8 J/molK.

Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

The speed of sound in an ideal gas at ${ T } _{ 1 }$ K and   ${ T } _{ 2 }$K  are $ { V } _{ 1 }$ and $ { V } _{ 2 }$ respectively. if the root mean square velocity of molecules of same gas at these temperatures are  $  { v } _{ rms1 }  $ and${ v } _{ rms1 }$ respectively, then 

  1. ${ v } _{ rms2 }={ v } _{ rms1 }\left( \dfrac { { v } _{ 2 } }{ { v } _{ 1 } } \right) $
  2. ${ v } _{ rms2 }={ v } _{ rms1 }\left( \dfrac { { v } _{ 1 } }{ { v } _{ 2 } } \right) $
  3. $ { v } _{ rms2 }={ v } _{ rms1 }\left( \sqrt { \dfrac { { v } _{ 2 } }{ { v } _{ 1 } } } \right) $
  4. $ { v } _{ rms2 }={ v } _{ rms1 }\left( \sqrt { \dfrac { { v } _{ 1 } }{ { v } _{ 2 } } } \right) $
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

The relation between velocity of sound in gas $(v)$ and r.m.s velocity of molecules of gas $v _{r.m.s}$ is

  1. $v=v _{r.m.s}(\gamma/ 3)^{1/2} $
  2. $v _{r.m.s}=v(2/3)^{1/2} $
  3. $v=v _{r.m.s} $
  4. $ v=v _{r.m.s}(3/\gamma)^{1/2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Velocity of sound in a gas is

$v=\sqrt{\dfrac{\gamma P}{\rho}}$

and from $P=\dfrac{1}{3}\rho v _{rms}^2$

$v _{rms}=\sqrt{\dfrac{3P}{\rho}}$
Thus

$\dfrac{v}{v _{rms}}=\sqrt{\dfrac{\gamma}{3}}$

Ans: A

Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

The velocity of sound in a gas at pressure $P$ and density $d$ is

  1. $\displaystyle v= \sqrt {\frac {\gamma P}{d}}$
  2. $\displaystyle v= \sqrt {\frac {P}{\gamma d}}$
  3. $\displaystyle v= \gamma \sqrt {\frac {P}{d}}$
  4. $\displaystyle v= \sqrt {\frac {2 P}{d}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle v= \sqrt {\frac {\gamma RT}{M}}$

$PV=RT$

$\displaystyle P\frac {M}{d}=RT$

$\displaystyle \frac {P}{d} = \frac {RT}{M}$

$\displaystyle v= \sqrt {\frac {\gamma P}{d}}$

Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

The velocities of sound at the same temperature in two monoatomic gases of densities $p _1$ and $p _2$ are $v _1$ and $v _2$ respectively. If $p _1/p _2 = 4$, then the value of $v _1/v _2$ is

  1. $\dfrac{1}{4}$
  2. $2$
  3. $\displaystyle \dfrac {1}{2}$
  4. $4$
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation

For velocity of sound in gas
$\displaystyle v=\sqrt {\frac {p\gamma }{p}}$

$[P$ is pressure and $p$ is density of gas, $\gamma$ is $C _p/C _v]$

Here, $\displaystyle v _1 = \sqrt {\frac {\gamma P}{p _1}}$ and $v _2 = \sqrt {\frac {\gamma P}{p _2}}$

$\displaystyle \frac {v _1}{v _2} = \sqrt {\frac {p _2}{p _1}} = \sqrt {\frac {1}{4}}=\frac {1}{2}$

Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

If the pressure of a fixed quantity of a gas is increased 4 times keeping the temperature constant, the r.m.s velocity will :

  1. get doubled

  2. get halved

  3. remain same

  4. get quadrupled
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

RMS velocity is independent of pressure. Hence velocity does not change with variations in pressure

The correct option is (c)

Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

With increase in temperature, the rms speed and wave speed in a gas

  1. increases with temperature

  2. decreases with temperature

  3. are independent of temperature

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

Both RMS speed and speed of sound in gas are directly proportional to temperature. Thus, both the speeds increases with temperature

The correct option is (a)