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 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

An ideal gas having initial pressure P, volume V and temperature T is allowed to expand adiabatically until its volume becomes $5.66$V while its temperature falls to $T/2$. How many degrees of freedom do the gas molecules have?

  1. 7
  2. $5$.

  3. 6

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Adiabatic equation of perfect gas is given as $TV^{r-1}=$ constant
$m=T _{1}V _{1}^{(r-1)}=T _{2}V _{2}^{(r-1)}$
$T _{1}=T _{1}V _{1}=V _{1}V _{2}=5.66\ V$
and $T _{2}=\dfrac{T}{2}$
$TV^{r-1}=\dfrac{T}{2}(5.66\ V)^{r-1}$
$2=5.66^{r-1}$
Taking $\log$ on both sides
$(r-1)\log 5.66=\log 2(r-1)$
$r=\dfrac{\log 2}{\log 5.66}=1+0.3010/0.75$
$r=1+0.4$
$r=1.4$ for $r=1.4$ Agree of freedom $=5$
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 has molar heat capacity $C = 4.5\ R$ in the process $PT = constant$. Find the number of degrees of freedom (n) of molecules in the gas.

  1. $n = 7$
  2. $n = 3$
  3. $n = 5$
  4. $n = 2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a process PT = constant, P * (PV/nR) = constant, so P^2 * V = constant. This is a polytropic process PV^x = constant with x = 1/2. Molar heat capacity C = R/(gamma-1) + R/(1-x). 4.5R = R/(2/f) + R/(1-0.5) = fR/2 + 2R. 4.5 = f/2 + 2, so f/2 = 2.5, f = 5.

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 degrees of freedom of a triatomic gas is? (consider moderate temperature)

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

The general epression for degree of freedom is $DOF=3N-n$

here, DOF means degree of freedom, N is number of particle, and n is the number of holonomic constraints.
for a triatomic molecule, the number of particle is 3 and since the separation between three atoms are fixed so, the number of constraints is 3.
hence, $DOF=(3\times 3)-3$
$DOF=9-3$
$DOF=6$

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

For gas, if the ratio of specific heats at constants pressure $P$ and constant volume $V$ is $\gamma $, then the value of degree of freedom is:

  1. $\dfrac{\gamma +1}{\gamma -1}$
  2. $\dfrac{\gamma -1}{\gamma +1}$
  3. $\dfrac{1}{2}(\gamma-1)$
  4. $\dfrac{2}{\gamma-1}$
Reveal answer Fill a bubble to check yourself
A 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

When an ideal monoatomic  gas is heated zt constant pressure , which of the following may be true

  1. $\dfrac {dU}{dQ} = \frac {3}{5}$
  2. $\dfrac {dW}{dQ} = \frac {2]}{5}$
  3. $\dfrac {dU}{dQ} = \frac {4}{5}$
  4. $dW + dU = dQ $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From First Law: dQ = dU + dW. This is always true for any process. For monatomic gas at constant pressure, dU = (3/2)nRdT and dW = PdV = nRdT, so dQ = (5/2)nRdT. Then dU/dQ = 3/5 and dW/dQ = 2/5, not 4/5. Option D is the fundamental First Law statement.

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

If $\gamma $ be the ration of specific heats of a perfect gas, the number of degree of freedom of a molecule of the gas is:

  1. $\dfrac{{25}}{2}\left( {\gamma - 1} \right)$
  2. $\dfrac{{3\gamma - 1}}{{2\gamma - 1}}$
  3. $\dfrac{2}{{\gamma - 1}}$
  4. $\dfrac{9}{2}(\gamma - 1)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The relationship between the adiabatic index gamma and degrees of freedom f is gamma = 1 + 2/f. Solving for f gives f = 2 / (gamma - 1).

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 monoatomic gas undergoes an isothermal expansion at temperature T during which its volume becomes 4 times. The work done on the gas and change in internal energy of the gas respectively is

  1. n RT Ln 4,0
    • n RT Ln 4,0
  3. n RT Ln 4 $\frac { 3 n R T } { 2 }$
  4. - n RT Ln 4, $\frac { 3 n R T } { 2 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\begin{array}{l} w=nRT\, \, \, \ln { \left( { \frac { { 4v } }{ v }  } \right)  }  \ =nRT\, \, \ln { 4 } \, \, \, \, \, \, & \, \, \, \Delta u=0 \end{array}$

$\therefore$ Option $A$ is correct.

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

Three perfect gases at absolute temperatures $T _1, T _2$ and $T _3$ are mixed. The masses of their molecules are $m _1, m _2$ and $m _3$ and the number of molecules are $n _1, n _2$ and $n _3$ respectively. Assuming no loss of energy, the final tempreture of the mixture is 

  1. $\dfrac{T _1 + T _2 + T _3}{3}$
  2. $\dfrac{n _1T _1 + n _2T _2 + T _3 T _3}{n _1 + n _2 + n _3}$
  3. $\dfrac{n _1T _1^2 + n _2T _2^2 + n _3 T _3^2}{n _1 T _1 + n _2 T _2 + n _3 T _3}$
  4. $\dfrac{n _1^2T _1^2 + n _2^2T _2^2 + n _3^2 T _3^2}{n _1 T _1 + n _2 T _2 + n _3 T _3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The final temperature of a mixture of non-reacting gases is the weighted average of their temperatures based on the number of moles (or molecules) of each gas, assuming equal degrees of freedom. The formula is T_final = (n1*T1 + n2*T2 + n3*T3) / (n1 + n2 + n3).

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 sampleof 192 g of gas in a container of volume 80$\mathrm { L }$ at atemperature of $402 ^ { \circ } \mathrm { C }$ and at a pressure of$4.2 \times 10 ^ { 5 } \mathrm { Pa }$ is 124.5$\mathrm { JK }$ . The number of thedegrees of freedom of the gas molecules is 

  1. 3

  2. 5

  3. 7

  4. 6
Reveal answer Fill a bubble to check yourself
A 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

Statement -1 : The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume.
and
Statement -2: The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.

  1. Statement - 1 is True, Statement -2 is True, Statement -2 is a correct explanation for Statements-1

  2. Statement - 1 is True, Statement -2 is True, Statement -2 is NOT a correct explanation for Statements-1

  3. Statement - 1 is True, Statement -2 is False

  4. Statement - 1 is False, Statement -2 is True
Reveal answer Fill a bubble to check yourself
A Correct answer