Kinetic Theory Test

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Kinetic Theory Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

The average energy per molecule of a triatomic gas at room temperature T is?

A
$$3kT$$

B
$$\dfrac{1}{2}kT$$

C
$$\dfrac{3}{2}kT$$

D
$$\dfrac{5}{2}kT$$

Solution

A triatomic (non-linear) gas molecule has $$6$$ degrees of freedom ($$3$$ translational, $$3$$ rotational and no vibrational) at room temperature.
According to the law of equipartition of energy, the average energy per molecule of a triatomic gas at room temperature T is
$$\bar{E}=\dfrac{1}{2}fKT=\dfrac{1}{2}6KT=3KT$$
Question 2
1 / -0

The value of universal gas constant is $$8.3\ J/mole/K$$, the mean kinetic energy of $$32gm$$ of oxygen at $$-73^oC$$ will be

A
$$480\ J$$

B
$$4980\ J$$

C
$$2490\ J$$

D
$$100\ J$$

Solution

$$R=8.3J/moleK$$ , atomic weight of $$nascent$$ oxygen is $$16$$
so number of moles $$n=\dfrac{32}{16}=2$$
Mean kinetic energy will be $$KE=\dfrac{nFRT}{2}$$
Where $$F$$ is degree of freedom which will be $$3$$ because $$O$$ is a mono-atomic molecule.
Temperature, $$T=-73+273=200K$$
So energy=$$\dfrac{2\times 3 \times 8.3 \times 200}{2}=4980Joule$$

So, Option B is correct.
Question 3
1 / -0

The lowest pressure (the best vaccum) that can be created in laboratory at $$20^{\circ}C$$ is $$10^{-10}\ mm$$ of $$Hg$$. At this pressure, the number of ideal gas molecules per $$cm^{3}$$ will be

A
$$3.22\times 10^{12}$$

B
$$1.61\times 10^{12}$$

C
$$3.29\times 10^{6}$$

D
$$3.22\times 10^{5}$$

Solution

For gaseous mixture at vaccum

$$P=10^{-10}mm=\dfrac{10^{-10}}{760}atm$$

$$V=10^{-3}\,litre$$

$$n=?$$

$$R=0.0821\,litre\,K^{-1}\,mol^{-1}$$

$$T=293\,K$$

$$PV=nRT$$

$$\therefore n=\dfrac{PV}{RT}=\dfrac{10^{-10}\times 10^{-3}}{760\times 0.0821 \times 293}=5.47 \times 10^{18}$$

$$\therefore$$ Number of molecule per $$mL=5.47 \times 10^{-18} \times 6.023 \times 10^{23}=3.29 \times 10^6\,molecule$$
Question 4
1 / -0

Under which of the following conditions is the law $$pV=RT$$ obeyed most closely by a real gas?

A
High pressure and high temperature

B
Low pressure and low temperature

C
Low pressure and high temperature

D
High pressure and low temperature

Solution

At low pressure and high temperature real gases behaves like ideal gases.
Question 5
1 / -0

The S.I. unit of universal gas constant is

A
$$Watt K^{-1}mol^{-1}$$

B
$$ N K^{-1}mol^{-1}$$

C
$$JK^{-1}mol^{-1}$$

D
$$erg K^{-1}mol^{-1}$$

Solution

From the relation $$R = \dfrac{2\Delta U}{3 nT}$$
where $$\Delta U$$ is the change in internal energy, $$n$$ is number of moles of gas and $$\Delta T$$ is change in temperature.
We get the S.I. unit of universal gas constant is $$JK^{-1}mol^{-1}$$.
Question 6
1 / -0

Which of the following is correct?
(Internal pressure in Van der Waal's equation)

A
$${ C }_{ V }={ \left( \cfrac { \partial U }{ \partial T } \right) }_{ P }\quad $$

B
$${ C }_{ P }={ \left( \cfrac { \partial H }{ \partial T } \right) }_{ V }\quad $$

C
$${ C }_{ P }-{ C }_{ V }=R$$

D
$${ \left( \cfrac { \partial U }{ \partial T } \right) }_{ t }=\cfrac { -a }{ { V }^{ 2 } } $$

Solution

$${ C }_{ P }-{ C }_{ V }=R$$ $$\text{ is the correct expression.}$$
Question 7
1 / -0

Two gases, carbon monoxide $$(CO)$$ and nitrogen $$(N_2)$$ at the same temperature, have kinetic energies $$E_1$$ and $$E_2$$ respectively. Then :

A
$$E_1 = E_2$$

B
$$E_1 > E_2$$

C
$$E_1 < E_2$$

D
$$E_1$$ and $$E_2$$ cannot be compared

Solution

The gases carbon monoxide (CO) and nitrogen $$(N_2)$$ are diatomic. so both have equal kinetic energy $$\dfrac{5}{2} kT$$ .i.e., = $$E_1=E_2$$
Question 8
1 / -0

At room temperature (27$$^0$$ C) the rms speed of the moleculesof certain diatomic gas is found to be 1920 ms$$^{-1}$$ then the molecule is:

A
$$H_2$$

B
$$F_2$$

C
$$O_2$$

D
$$Cl_2$$

Solution

Let the room temperature is $$T = 27^0C=27+273=300K$$
Now, $$V_{rms}=\sqrt{\dfrac{3RT}{m}}$$
$$\Rightarrow M=\dfrac{3RT}{V_{rms}^2}$$
By putting the value we get,
$$M=\dfrac{3\times8.314\times300}{1920^2}=2\times10^{-3}kg=2g$$
Thus, it is an Hydrogen.
Question 9
1 / -0

At what temperature does the average transnational kinetic energy of a molecule in a gas become equal to kinetic energy of an electron accelerated from rest through a potential difference of $$1$$ volt? ($$k=1.38 \times 10^{-23}J/K)$$

A
$$3770K$$

B
$$7370 K$$

C
$$7730 K$$

D
$$7330 K$$

Solution

Given, $$K=1.38\times^{-23}J/K$$
Potential difference $$V =1$$ volt
So, the average translational energy is given by the equipartition theorem,
$$E=1.5kT$$
where $$E = 1eV$$
$$\Rightarrow 1\times 1.6\times 10^{-19}=1.5\times kT$$
$$\Rightarrow T=\dfrac{1.6\times 10^{-19}}{1.5\times1.38\times10^{-23}}=7730K$$
Question 10
1 / -0

Gas exerts pressure on the walls of container because the molecules-

A
Are loosing the kinetic energy

B
Are getting stuck to the walls

C
Are transferring their momentum to walls

D
Are accelerated toward walls.

Solution

Gas molecules are in random motion having some momentum and while colliding with the walls they transfer their momentum to the walls and this collective transfer of momentum from all the molecules to the walls appears as pressure exerted by gas on the container wall.

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Re-Attempt Weekly Quiz Competition

Kinetic Theory Test - 19

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Kinetic Theory Test - 19

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SHARING IS CARING

Question 1

$$3kT$$

$$\dfrac{1}{2}kT$$

$$\dfrac{3}{2}kT$$

$$\dfrac{5}{2}kT$$

Solution

Question 2

$$480\ J$$

$$4980\ J$$

$$2490\ J$$

$$100\ J$$

Solution

Question 3

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

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

$$3.29\times 10^{6}$$

$$3.22\times 10^{5}$$

Solution

Question 4

High pressure and high temperature

Low pressure and low temperature

Low pressure and high temperature

High pressure and low temperature

Solution

Question 5

$$Watt K^{-1}mol^{-1}$$

$$ N K^{-1}mol^{-1}$$

$$JK^{-1}mol^{-1}$$

$$erg K^{-1}mol^{-1}$$

Solution

Question 6

$${ C }_{ V }={ \left( \cfrac { \partial U }{ \partial T } \right) }_{ P }\quad $$

$${ C }_{ P }={ \left( \cfrac { \partial H }{ \partial T } \right) }_{ V }\quad $$

$${ C }_{ P }-{ C }_{ V }=R$$

$${ \left( \cfrac { \partial U }{ \partial T } \right) }_{ t }=\cfrac { -a }{ { V }^{ 2 } } $$

Solution

Question 7

$$E_1 = E_2$$

$$E_1 > E_2$$

$$E_1 < E_2$$

$$E_1$$ and $$E_2$$ cannot be compared

Solution

Question 8

$$H_2$$

$$F_2$$

$$O_2$$

$$Cl_2$$

Solution

Question 9

$$3770K$$

$$7370 K$$

$$7730 K$$

$$7330 K$$

Solution

Question 10

Are loosing the kinetic energy

Are getting stuck to the walls

Are transferring their momentum to walls

Are accelerated toward walls.

Solution

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