Kinetic Theory Test

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Kinetic Theory Test - 56

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Question 1
1 / -0

The molecules of a given mass of gas have rms velocity $$200\ ms^{-1}$$ at $$27^{\circ}C$$ and $$10^5\ Nm^{-2}$$ pressure. When the absolute temperature is doubled and the pressure is halved, the rms speed of the molecules of the same gas is:

A
$$200\ ms^{-1}$$

B
$$400\ ms^{-1}$$

C
$$200\sqrt{2}\ ms^{-1}$$

D
$$400\sqrt{2}\ ms^{-1}$$

Solution
Question 2
1 / -0

In a thermodynamic system, working substance is ideal gas, its internal energy is in the form of

A
kinetic energy

B
kinetic and potential energy

C
potential energy

D
None of the above

Solution
Question 3
1 / -0

For gas, if the ratio of specific heats at constants pressure $$P$$ and constant volume $$V$$ is $$\gamma $$, then the value of degree of freedom is:

A
$$\dfrac{\gamma +1}{\gamma -1}$$

B
$$\dfrac{\gamma -1}{\gamma +1}$$

C
$$\dfrac{1}{2}(\gamma-1)$$

D
$$\dfrac{2}{\gamma-1}$$

Solution
Question 4
1 / -0

The speed of a longitudinal wave in a mixture containing 4 moles of He and 1 mole of Ne at 300 K will be

A
930 m/s

B
541 m/s

C
498 m/s

D
None of these

Solution

The mixture contains $$n_1=4\ mol$$ of $$He$$ and $$n_2=4\ mole$$ of $$Ne$$ act. $$T=300\ K$$.
Forth $$He$$ and $$Ne$$ are monoatomic, so we take $$r$$ mix $$=5/3\quad \left [r=\dfrac {cp}{cv}\right]$$
$$M'=\dfrac {M_1n_1+M_2n_2}{n_1+n_2}$$
$$=\dfrac {4\times 4+20\times 1}{4+1}=\dfrac {24}{5}=4.8\ g/mol$$
$$=4.8\times 10^{-3}\ kg/mol$$
$$\therefore \ $$ Speed of sound through mixture
$$v=\sqrt {\dfrac {vRT}{M'}}=\sqrt {\dfrac {5}{3}\times \dfrac {8.3\times 300}{4.8\times 10^{-3}}}\sim 929.83\ m/s$$
Question 5
1 / -0

The internal energy of an ideal gas increases during an isothermal process when the gas is

A
Expanded by adding more molecules to it

B
Expanded by adding more heat to it

C
Expanded against zero pressure

D
Compressed by doing work on it

Solution

Internal energy of isotherma process
$$v=\dfrac{f}{2} \times NKT$$
$$\Rightarrow v\propto NT$$
T is constant (Isothermal process $$v \propto N$$ i.e., Internal energy increases by increasing number of molecules(N).
Question 6
1 / -0

One-gram mole of nitrogen occupies $$ 2 \times 10^4 $$ cc at a pressure of $$ 10^6 dynes/cm^2 $$. The average energy of a nitrogen molecule (in erg) will be:$$ (Avogadro's number = 6 \times 10^25 ) $$

A
$$ 14 \times 10^{-13} $$

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

C
$$ 10^6 $$

D
$$ 2 \times 10^6 $$

Solution
Question 7
1 / -0

In a process the pressure of gas is inversely proportional to the square of volume If temperature of the gas is increased then work done by the gas

A
Is positive

B
Is negative

C
Is zero

D
May be positive

Solution
Question 8
1 / -0

In a thermodynamic system, working substance is ideal gas, its internal energy is in the form of

A
Kinetic energy

B
Kinetic and potential energy

C
Potential energy

D
None of the above

Solution

Kinetic theory states that distance between two particle is infinity and therefore potential energy is zero. Hence internal energy depends only on kinetic energy. So answer should be A.
Question 9
1 / -0

$$T_1$$ 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

A
$$A_1 > A_2$$

B
$$A_1 < A_2$$

C
A_1 = A_2$$

D
$$A_1=\sqrt {A_2}$$
Question 10
1 / -0

The total kinetic energy of $$8$$ litres of helium molecules at $$5$$ atmosphere pressure will be
($$1$$ atmosphere = $${ 1.013\times 10 }^{ 5 }$$pascal)

A
$$\text{607 J}$$

B
$$\text{6078 J}$$

C
$$\text{607 erg}$$

D
$$\text{6078 erg}$$

Solution

$$Given:$$ The total K.E of 8 litres of helium molecules at 5 atmosphere pressure. ($$1 atmosphere=1.013\times10^{5} pascal)$$
$$Solution:$$ We know that,
$$\mathrm{E}_{\mathrm{k}}=\dfrac{3}{2} \mathrm{PV}$$
$$=\dfrac{3}{2} \times 5 \times 8 \times 1.013 \times 10^{5}=60.78 \times 10^{5}=6078 \mathrm{~J}$$
$$So,the$$ $$correct$$ $$option:B$$