Tag: kinetic theory of gases

Quizzes (6) Questions (57)

Questions Related to kinetic theory of gases

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

At what temperature volume of an ideal gas at $0^oC$  becomes triple by keeping pressure constant

  1. $546^oC$

  2. $182^oC$

  3. $819^oC$

  4. $646^oC$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using Charles's Law (V1/T1 = V2/T2) at constant pressure, if V2 = 3*V1, then T2 = 3*T1. Given T1 = 0 C = 273 K, T2 = 3 * 273 = 819 K. Converting back to Celsius, 819 - 273 = 546 C.

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

A container with insulating wall is divided into two equal parts by a partition fitted with a vaive.One part is filled with an ideal gas at pressure P and temperature T, whereas the other part is one part is  completely evacuated. If the valve is suddenly opened, the pressure and temperature of gas will be: 

  1. $P , \cfrac { T } { 2 }$

  2. $\cfrac { P } { 2 } , T$

  3. $\cfrac { P } { 2 } , \cfrac { T } { 2 }$

  4. $P , T$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is a free expansion (Joule expansion) into a vacuum. Since the walls are insulating (adiabatic) and no work is done (expansion against vacuum), the internal energy remains constant, meaning temperature T remains constant. The volume doubles, so by PV = nRT, the pressure must halve to P/2.

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

The number of air molecules in a $(5m\times5m\times4m)$ room at standard temperature and pressure is of the order of

  1. $6\times10^{23}$

  2. $3\times10^{24}$

  3. $3\times10^{27}$

  4. $6\times10^{30}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume V = 5*5*4 = 100 m^3. At STP, 1 mole occupies 22.4 liters (0.0224 m^3). Number of moles n = 100 / 0.0224 approx 4464 moles. Number of molecules = n * Avogadro's number = 4464 * 6e23 approx 2.68e27, which is of the order of 10^27.

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

The relation PV=RT can describe the behavior of a real gas at :

  1. high temperature and high pressure

  2. high temperature and low pressure

  3. low temperature and low pressure

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

PV=RT is ideal gas equation and gases behave ideally only at high temperature and low pressure.
Therefore option(B).

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

A real gas behaves as an ideal gas :

  1. at very low pressure and high temperature

  2. high pressure and low temperature

  3. high temperature and high pressure

  4. low pressure and low temperature
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Real gas obeys vanderwaals equation 
$\left( p+\dfrac { n^{ 2 }a }{ V^{ 2 } }  \right) \left( V-nb \right) =nRT$
at high temperature and low pressure
Van der waal equation becomes approximately PV=nRT
Hence gases behave ideally at high temperature and low pressure.
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 a real gas can be expressed as $(P + \dfrac{a}{V _2}) (V - b) = cT$, where P is the pressure, V the volume, T the absolute temperature and a, b, c are constants. What are the dimensions of 'a'-

  1. $M^0 L^3 T^{-2}$

  2. $ M L^{-2} T^5$

  3. $M L^5 T{-2}$

  4. $M^0 L^3 T^0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\left( {p + \frac{a}{{{V _2}}}} \right)\left( {v - b} \right) = cT$

$p$ is pressure, $V$ is volume and $T$ is temperature
$\begin{array}{l} p=\frac { F }{ A } =\frac { { ML{ T^{ -2 } } } }{ { { L^{ 2 } } } } =M{ L^{ -1 } }{ T^{ -2 } } \ V={ L^{ 3 } } \end{array}$
We cannot add or subtract quantities of different dimensions.
$\begin{array}{l} \therefore p=\frac { a }{ { { V^{ 2 } } } }  \ \Rightarrow a=\frac { p }{ { { V^{ 2 } } } } =\frac { { M{ L^{ -1 } }{ T^{ -2 } } } }{ { { { \left( { { L^{ 3 } } } \right)  }^{ 2 } } } } =M{ L^{ 5 } }{ T^{ -2 } } \end{array}$
Hence, Option $C$ is correct.

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

Diatomic gas at pressure `P' and volume `V' is compressed adiabatically to 1/32 times the original volume. Then
the final pressure is

  1. P/32

  2. 32 P

  3. 128 P

  4. P/128
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For adiabatic processes, P * V^gamma = constant. For a diatomic gas, gamma = 1.4 or 7/5. P2 = P1 * (V1/V2)^gamma. Here V1/V2 = 32. P2 = P * (32)^(7/5) = P * (2^5)^(7/5) = P * 2^7 = 128P.