Kinetic Theory Test

Result

Kinetic Theory Test - 79

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Weekly Quiz Competition

Question 1
1 / -0

A particle moving along x-axis is acted upon by a single force $$F=F_0e^{-kx}$$, where $$F_0$$ and K and constants. The particle is released from rest at x=0. It will attain a maximum KE of

A
$$\frac{F_0}{K} $$

B
$$\frac{F_0}{e^K} $$

C
$$KF_0$$

D
$$Ke^KF_0$$

Solution
Question 2
1 / -0

Figure shows a hypothetical speed distribution for particles of a certain gas $$P ( v ) = C r ^ { 2 } \text { for } 0 < v \leq v _ { 0 } \text { and } P ( v ) = 0 \text { for } v > V _ { 0 }$$

A
$$C = 3 / V ^ { 3 }$$

B
average speed =$$0.750 \mathrm { V } _ { 0 }$$

C
rms speed=$$0.775 \mathrm { V } _ { 0 }$$

D
$$C = 3 / V ^ { 2 }$$
Question 3
1 / -0

A gas of molecule of mass M at the surface of the Earth has kinetic energy equivalent to $${0^0}C$$. If it were to go up straight without colliding with any other molecules, how high it would rise? Assuming that the height attained is much less than radius of the earth.

A
$$0$$

B
$$\frac{{273{k_B}}}{{2{M_g}}}$$

C
$$\frac{{546{k_B}}}{{3{M_g}}}$$

D
$$\frac{{819{k_B}}}{{2{M_g}}}$$

Solution
Question 4
1 / -0

N moles of an ideal diatomic gas is contained in a cylinder at temperature $$T.$$ On supplying some heat to cylinder, $$N/3$$ moles of gas disassociated into atoms while temperature remains constant. Heat supplied to the gas is

A
$$\dfrac {NRT}{3}$$

B
$$\dfrac {5NRT}{2}$$

C
$$\dfrac {8NRT}{3}$$

D
$$\dfrac {NRT}{6}$$

Solution
Question 5
1 / -0

The respective speeds of the molecules are $$1,2,3,4$$ and $$5\,km, {s}^{-1}$$. The ratio of their r.m.s. velocity and the average velocity will be

A
$$\sqrt{11} : 3$$

B
$$3 : \sqrt{11 }$$

C
$$1 :2$$

D
$$3 : 4$$

Solution
Question 6
1 / -0

A box contains N molecules of a perfact gas at temperature $$T_{1}$$ and pressure $$P_{1}$$. The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure is $$P_{2}$$ and temperature $$T_{2}$$, then

A
$$P_{2}=P_{1},T_{2}=T_{1}$$

B
$$P_{2}=P_{1},T_{2}=\cfrac{T_{1}}{2}$$

C
$$P_{2}=2P_{1},T_{2}=T_{1}$$

D
$$P_{2}=2P_{1},T_{2}=\cfrac{T_{1}}{2}$$

Solution
Question 7
1 / -0

One mole of an ideal gas undergoes a cyclic change as shown in the figure. The process AB is isothermal. The pressure and volume at point A is $$2.1 \times {10^5}$$ and 22.4 liters, respectively. The temperature at C is

A
$${10^0}{\text{C}}$$

B
273 K

C
0 K

D
$${27^0}{\text{C}}$$

Solution
Question 8
1 / -0

The pressure of the gas contained in a closed vessel is increased by $$0.4\%$$ when heated by $$1^oC$$. The initial temperature of the gas must be

A
$$1250 K$$

B
$$250 K$$

C
$$2500 K$$

D
$$25^oC$$

Solution
Question 9
1 / -0

Energy associated with each molecule per degree of freedom of a system at room temperature ($$27^{o}C$$) will be ($$k$$ is Boltzmann;s constant)

A
$$150\ k$$

B
$$(27/2)\ k$$

C
$$1/2\ R$$

D
$$none\ of\ these$$

Solution
Question 10
1 / -0

For a particle moving along x-axis, acceleration is given as $$a=2v^2$$. If the speed of the particle is $$v_0$$ at $$x=0$$, find speed as a function of $$x$$.

A
$$v_0e^{2x}$$

B
$$v_0e^{-2x}$$

C
$$v_0e^{-4x}$$

D
$$v_0e^{4x}$$

Solution