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

The SI unit for the coefficient of cubical expansion is

  1. $^\circ C$

  2. $per^\circ C$

  3. $cm^{2}/^\circ C$

  4. none of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
The SI unit of coefficient of cubical expansion is $K^{-1}$
$\gamma =\cfrac { 1 }{ V } \cfrac { dV }{ dT } =\cfrac { 1 }{ { metre }^{ 3 } } \cfrac { { metre }^{ 3 } }{ K } ={ K }^{ -1 }$
Multiple choice physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density $\rho$ remains uniform throughout the volume. The rate of fractional change in density $\left(\dfrac{1}{p}\dfrac{d\rho}{dt}\right)$ is constant. The velocity v of any point on the surface of the expanding sphere is proportional to.

  1. R

  2. $R^3$

  3. $\dfrac{1}{R}$

  4. $R^{2/3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Density rho = M / V = M / ((4/3) * pi * R^3). Taking the logarithmic derivative with respect to time, (1/rho) * (d_rho/dt) = -3 * (1/R) * (dR/dt). Since the fractional change in density is constant, (1/R) * (dR/dt) must be constant. The velocity of the surface is v = dR/dt, so v = constant * R.

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. <span>$2|T$</span>

  3. <span>$3|T$</span>

  4. <span>$4|T$</span>
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

$T _1$ is the temperature of oxygen enclosed in a cylinder. The temperature is increased to $T _2$ and Maxwellan distribution curves for $O _2$ at temperature $T _1$ and $T _2$ are plotted. If $A _1$ and $A _2$ are the areas under the curves and the speed axis, in both cases , then 

  1. $A _1 &gt; A _2$

  2. $A _1 &lt; A _2$

  3. A_1 = A_2$

  4. $A _1=\sqrt {A _2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 mixture of ideal gases 7 kg of nitrogen and 11 Kg of $ CO _2 $ then (Take $\gamma$ for nitrogen and $CO _2$ as 1.4 and 1.3 respectively)

  1. Equivalent molecular weight of the mixture is 36.

  2. Equivalent molecular weight of the mixture is 18.

  3. $ \gamma $ for the mixture is 5/2

  4. $ \gamma $ for the mixture is 47/35
Reveal answer Fill a bubble to check yourself
A,D Correct answer
Multiple choice physics kinetic theory maxwell-boltzmann speed distribution function behavior of perfect gas and kinetic theory kinetic theory of matter

$3$ mole of gas ''X"  and $2$ moles of gas "Y" enters from end "P" and "Q" of the cylinder respectively. The cylinder has the area of cross section , shown as
under 
The length of the cylinder is $150cm$. The gas "X" intermixes with gas "Y" at the point . If the molecular weight of the gases X and Y is $20$ and $80$ respectively, then what will be the distance of point A from Q?

  1. $75cm$

  2. $50cm$

  3. $37.5$

  4. $90cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\begin{array}{l} \frac { { rx } }{ { ry } } =\frac { { { w _{ x } } } }{ { { n _{ y } } } } \sqrt { \frac { { { M _{ y } } } }{ { { M _{ x } } } }  }  \ =\frac { 3 }{ 2 } \sqrt { \frac { { 80 } }{ { 20 } }  } =\frac { 3 }{ 1 } =3:1 \ \therefore \frac { { dis\tan  ce\, \, travelled\, \, by\, \, gas\, \, X } }{ { dis\tan  ce\, \, travelled\, \, by\, \, gas\, \, Y } } =3:1 \ \therefore dis\tan  ce\, \, of\, \, A\, \, from\, \, Q=\frac { { 150 } }{ 3 } =50\, \, cms \end{array}$

Hence, OPtion $B$ is correct.

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

The lowest pressure(the best Vaccum) that can be created in laboratory at 27 degree is $10^{-11} $ mm of Hg. At this pressure, the number of ideal gass molecules per $cm^{3}$ will be

  1. $3.22 \times 10 ^{12} $

  2. $1.61 \times 10 ^{12} $

  3. $3.21 \times 10 ^{6} $

  4. $3.22 \times 10 ^{5} $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Use the ideal gas law PV = NkT, where N/V = P / (kT). Convert pressure to Pascals (1 mm Hg = 133.322 Pa) and temperature to Kelvin (300K). Calculate the number density N/V.