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 measurement and effects of heat thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

An inflated rubber balloon contains one mole of an ideal gas. Has a pressure p, volume V and temperature T. if the temperature rises to 1.1 T, and the volume is increase to 1.05 V, the final pressure will be:

  1. 1.04p

  2. 1.2 p

  3. less than p

  4. between p and 1.1.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$PV=nRT\rightarrow (1)\ P _1(1.05V)=nR(1.1T)\rightarrow (2)\ \Rightarrow (1)\div(2)\ \Rightarrow \cfrac{P}{1.05P _1}=\cfrac{1}{1.1}\ \Rightarrow P _1=\cfrac{1.1P}{1.05}=1.047P$

Multiple choice physics measurement and effects of heat thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

If $T$ represent the absolute temperature of an ideal gas, the volume coefficient of thermal expansion at constant pressure, is :

  1. $T$
  2. $T^2$
  3. $1/T$
  4. $1/T^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From the definition of $\gamma _p$ 


We have $V _t=V _0(1+\gamma _pt)$..........(1) 

Again from Charle's law, $V _t=V _0(1+\dfrac{1}{T}t)$...........(2)  

Comparing (1) and (2), 

$\gamma _p=\dfrac{1}{T}$

Hence,option C is correct.

Multiple choice physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

One mole of n ideal monatomic  gas undergoes the following four reversible processes:
Step I: It is first compresses adiabatically from volume $V _1$ to $1m^3$.
Step II: then expanded isothermally to volume $10 m^3$.
Step III: then expanded adiabatically to volume $V _3$.
Step IV: then compressed isothermally to volume $V _1$.
If the efficiency of the above cycle is $3/4$ then V, is

  1. $2 m^3$
  2. $4 m^3$
  3. $6 m^3$
  4. $8 m^3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The efficiency of a Carnot-like cycle involving adiabatic and isothermal steps is 1 - (T_cold / T_hot). For an ideal gas, the temperature ratio is related to volume ratios via adiabatic relations (T * V^(gamma-1) = constant). Given efficiency 3/4, the ratio of temperatures is 1/4, which allows solving for V3 in terms of V1.

Multiple choice physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases
an ideal gas is expanding such that $PT^2$ $=costant$ The coefficient of volume expansion of the gas is__? 
  1. $1|T$
  2. $2|T$
  3. $3|T$
  4. $4|T$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For an ideal gas, PV = nRT. Given PT^2 = constant, substitute P = nRT/V into the equation to get (nRT/V) * T^2 = constant, which implies T^3 / V = constant, or V proportional to T^3. The coefficient of volume expansion gamma is (1/V) * (dV/dT). Differentiating V = k * T^3 gives dV/dT = 3 * k * T^2, so gamma = (3 * k * T^2) / (k * T^3) = 3/T.

Multiple choice physics kinetic theory maxwell-boltzmann speed distribution function behavior of perfect gas and kinetic theory kinetic theory of matter

Hydrogen is a diatomic gas. Its molar specific heat at constant volume is very nearly

  1. $\frac { 3 R } { 2 }$
  2. $\frac { 5 R } { 2 }$
  3. $\frac { 7 R } { 2 }$

  4. (b) or (c) depending on the temperature.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a diatomic gas like hydrogen, the molar specific heat at constant volume depends on the temperature. At low temperatures, only translational degrees of freedom are active (3R/2). At moderate temperatures, rotational degrees of freedom are active (5R/2). At very high temperatures, vibrational degrees of freedom may also contribute (7R/2).

Multiple choice physics kinetic theory maxwell-boltzmann speed distribution function behavior of perfect gas and kinetic theory kinetic theory of matter

let A and B the two gases and given :
$\frac{{T} _{A}}{{M} _{A}}$ = 4. $\frac{{T} _{B}}{{M} _{B}}$  Where T is the temperature and M is molecular mass. If ${C} _{A}$ and  ${C} _{B}$ are the r.m.s. speed, then the ratio $\frac{{C} _{A}}{{C} _{B}}$ will be equal to:

  1. 2

  2. 4

  3. 1

  4. 0.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The rms speed C is given by sqrt(3RT/M). The ratio C_A / C_B = sqrt((T_A / M_A) / (T_B / M_B)). Given T_A / M_A = 4 * (T_B / M_B), the ratio is sqrt(4) = 2.

Multiple choice physics kinetic theory maxwell-boltzmann speed distribution function behavior of perfect gas and kinetic theory kinetic theory of matter

A sample of gas is at $0^{\circ}C$. To what temperature must it be raised in order to double the rms speed of its molecules?

  1. $102^{\circ}C$
  2. $273^{\circ}C$
  3. $819^{\circ}C$
  4. $1092^{\circ}C$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The rms speed C is proportional to sqrt(T). If the speed doubles, the temperature must increase by a factor of 2^2 = 4. Initial temperature = 273K. Final temperature = 4 * 273K = 1092K. In Celsius, this is 1092 - 273 = 819C.

Multiple choice physics kinetic theory maxwell-boltzmann speed distribution function behavior of perfect gas and kinetic theory kinetic theory of matter

2 moles of an ideal monoatomic gas at temperature $T _0$ is mixed wth 4 moles of another ideal monoatomic gas at temperature $2T _0$ then  the temperature of the mixture is:

  1. $\frac{5}{3} T _0$
  2. $\frac{3}{2} T _0$
  3. $\frac{4}{3} T _0$
  4. $\frac{5}{4} T _0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a mixture of gases, the final temperature T_mix = (n1*T1 + n2*T2) / (n1 + n2). Here, n1=2, T1=T0, n2=4, T2=2T0. T_mix = (2*T0 + 4*2T0) / (2 + 4) = (2T0 + 8T0) / 6 = 10T0 / 6 = 5/3 * T0.

Multiple choice physics kinetic theory maxwell-boltzmann speed distribution function behavior of perfect gas and kinetic theory kinetic theory of matter

In two vessels of the same volume, atomic hydrogen and helium with pressure 1 atm and 2 atm are filled. If temperature of both the same is the same, then the average speed of hydrogen atom $v _H$ will be related to helium $v _{He}$ as

  1. $v _{H}$ $= \sqrt{2}$ $v _{He}$
  2. $v _H$ $=$ $v _{He}$
  3. $v _H$ $=$ 2$v _{He}$
  4. $v _H$ $=$ $\dfrac{v _{He}}{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By Maxwell's speed distribution, $<v>\alpha \sqrt { \dfrac { RT }{ M }  } $. Since the temperature of two gases is same, hence


$<v>\alpha \sqrt { \dfrac { 1 }{ M }  } $

Also, ${ M } _{ He }=4{ M } _{ H }$

Hence, $<{ v } _{ H }>=2<{ v } _{ He }>$

Answer is option C.

Multiple choice physics kinetic theory maxwell-boltzmann speed distribution function behavior of perfect gas and kinetic theory kinetic theory of matter

Average kinetic energy of a gas molecule is

  1. Inversely proportional to the square of its absolute temperature

  2. Directly proportional to the square root of its absolute temperature

  3. Directly proportional to its absolute temperature

  4. Directly proportional to square of absolute temperature
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The average kinetic energy of a gas molecule is given by (3/2)kT, where k is the Boltzmann constant and T is the absolute temperature. Thus, it is directly proportional to the absolute temperature.

Multiple choice physics kinetic theory maxwell-boltzmann speed distribution function behavior of perfect gas and kinetic theory kinetic theory of matter

Maxwell's laws of distribution of velocities shows that

  1. the number of molecules with most probable velocity is very large

  2. the number of molecules with most probable velocity is small

  3. the number of molecules with most probable velocity is zero

  4. the number of molecules with most probable velocity is exactly equal to 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The form of Maxwell's velocity distribution function is gaussian type. So the maximum of this function represents the speed at which most of the molecules travel. This speed is known as most probable speed.

Multiple choice physics kinetic theory maxwell-boltzmann speed distribution function behavior of perfect gas and kinetic theory kinetic theory of matter

The average velocity of the molecules in a gas in equilibrium is

  1. proportional to $\sqrt{T}$

  2. proportional to T
  3. proportional to $T^{2}$

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

the average velocity of the gas molecules = $\sqrt{\frac{8RT}{\pi M}}$
so clearly, the average velocity $\alpha \sqrt{T}$
So, A is the correct answer.
Note that T is the temperature in Kelvins

Multiple choice physics kinetic theory maxwell-boltzmann speed distribution function behavior of perfect gas and kinetic theory kinetic theory of matter

The average kinetic energy of a gas molecule at ${27}^{o}C$ is $6.21\times {10}^{-21}J$, then its average kinetic energy at ${227}^{o}C$ is:

  1. $10.35\times {10}^{-21}J$
  2. ${11.35}\times {10}^{-21}J$
  3. $52.2\times {10}^{-21}J$
  4. $5.22\times {10}^{-21}J$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average kinetic energy of gas molecules $\propto$ Temperature (Absolute)
$\cfrac{K.E(at\quad {227}^{o}C)}{K.E (at\quad {27}^{o}C)}=\cfrac{273+227}{273+27}=\cfrac{500}{300}=\cfrac{5}{3}$
$K.E({227}^{o})=\cfrac{5}{3}\times 6.21\times {10}^{-21}J=10.35\times {10}^{-21}J$

Multiple choice physics kinetic theory maxwell-boltzmann speed distribution function behavior of perfect gas and kinetic theory kinetic theory of matter

For a given gas, which of the following relationships is correct at a given temp?

  1. $u _{rms} > u _{av} > u _{mp}$
  2. $u _{rms} < u _{av} < u _{mp}$
  3. $u _{rms} > u _{av} < u _{mp}$
  4. $u _{rms} < u _{av} > u _{mp}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$u _{rms} = $ Root mean square velocity
$u _{ar}= $Average velocity 
$u _{mp} $= Most probable velocity
$u _{mp}:u _{ar}:u _{rms}= 1: 1.128: 1224$
$\therefore u _{rms} > u _{ar} > u _{mp}$