Kinetic Theory Test

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Kinetic Theory Test - 69

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Weekly Quiz Competition

Question 1
1 / -0

The average kinetic energy of a gas molecule at $$27^oC$$ is $$6.21\times 10^{-21}\ J$$. Its average kinetic energy at $$227^oC$$ will be :

A
$$52.2\times 10^{-21}\ J$$

B
$$5.22\times 10^{-21}\ J$$

C
$$10.35\times 10^{-21}\ J$$

D
$$11.35\times 10^{-21}\ J$$

Solution
Question 2
1 / -0

For which of the following ideal gas $${C}_{V,m}$$ is independent of temperature?

A
$$He$$

B
$${H}_{2}$$

C
$$CO$$

D
$${SO}_{2}$$

Solution

$${C}_{v,m}$$ molar heat capacity at constant volume.

It is heat required to increase the temperature of $$1$$ mole of the gas by $$1K$$.

But for inert gases, it is independent of temperature.

Option A is correct.
Question 3
1 / -0

Reducing the pressure from $$1.0$$ atm to $$0.5$$ atm would change the number of molecules in one mole of ammonia to?

A
$$75\%$$ of initial value

B
$$50\%$$ of initial value

C
$$25\%$$ of initial value

D
None of these

Solution

Pressure is decreased from $$1$$ atm to $$0.5$$ atm i.e., pressure increased or decreased doesn't affect the mole of ammonia
i.e., the no. of molecules in $$1$$ mole of ammonia won't change$$=6.022\times 10^{23}$$.
Question 4
1 / -0

A quantity of $$10$$g of a gas at $$1$$ atm pressure is cooled from $$273^o$$C to $$273$$K keeping its volume constant, the final pressure of the gas will be?

A
$$273$$ atm

B
$$0.5$$ atm

C
$$0.2$$ atm

D
$$0.1$$ atm

Solution

$$\dfrac{P_1}{T_1}=\dfrac{P_2}{T_2}$$

$$\dfrac{1}{546}=\dfrac{P_2}{273}$$

$$P_2=\dfrac{273}{546}$$

$$P_2=\dfrac{1}{2}=0.5$$ atm.

Answer option B.
Question 5
1 / -0

At what temperature the $$KE$$ of gas molecule is half that of its volue at $$27^oC$$?

A
$$13.5^oC$$

B
$$150^oC$$

C
$$150\ K$$

D
$$-123\ K$$

Solution
Question 6
1 / -0

The average translation kinetic energy of $$O_2$$ (molar mass $$32$$) molecules at a particular temperature is $$0.048\ eV$$. The translational kinetic energy of $$N_2$$ (molar mass $$28$$) molecules in $$eV$$ at the temperature is :

A
$$0.0015$$

B
$$0.003$$

C
$$0.048$$

D
$$0.768$$

Solution
Question 7
1 / -0

The heat capacity of air is $$20\ J/K/$$mol. The amount of heat, required to heat the room through $$1^o$$, assuming the amount of air in the room to be $$29\ kg$$, is

A
$$20\ kJ$$

B
$$-20\ J$$

C
$$200\ J$$

D
$$-200\ kJ$$

Solution

Dry air contains $$21 \%$$ oxygen and $$78 \% $$ nitrogen.

Thus molar mass of air = 29 g

The amount of heat required = $$ n(moles) \times C \times \triangle T = \dfrac{29000}{29} \times 20 \times 1 = 20k J$$
Question 8
1 / -0

The energy density U / V of an ideal monoatomic gas is related to its pressure P as

A
$$ \dfrac {U}{V} = 3P $$

B
$$ \dfrac {U}{V} = \dfrac {3}{2} P $$

C
$$ \dfrac {U}{V} = \dfrac {P}{3} $$

D
$$ \dfrac {U}{V} = \dfrac {5}{2} P $$

Solution

$$PV=RT$$

$$U= \dfrac{3RT}{2}$$

$$U$$ is the energy of gas

$$U= \dfrac{3PV}{2}$$

$$\dfrac{U}{V}= \dfrac{3P}{2}$$

$$\dfrac{U}{V}$$ is the energy density
Question 9
1 / -0

The curve in figure represents potential energy(U) in between two atoms in a diatomic molecule as a function of distance 'x' between atoms. The atoms are:

A
Attracted when x lies between 'A' and 'B' and repelled when x lies between B and C

B
Attracted when x lies between B and C and repelled when x lies between A and B

C
Attracted when they reach B

D
Repelled when they reach B

Solution
Question 10
1 / -0

The ratio of average translational kinetic energy to rotational kinetic energy of a diatomic molecule at temperature $$T$$ is :

A
$$3$$

B
$$7/5$$

C
$$5/3$$

D
$$3/2$$

Solution