Kinetic Theory Test

Result

Kinetic Theory Test - 59

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Weekly Quiz Competition

Question 1
1 / -0

Select the correct statement

A
The average KE of an ideal gas in calories per mole is approximately equal to its absolute temperature

B
The average KE of an ideal gas in calories per mole is approximately equal to two times its absolute temperature

C
The average KE of an ideal gas in calories per mole is approximately equal to three times its absolute temperature

D
The average KE of an ideal gas in calories per mole is approximately equal to 1.5 times its absolute temperature

Solution
Question 2
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A gas mixture contains 8 moles of oxygen and 2 mole of argon at room temperature T. The total energy of the mixture is

A
11 RT

B
23 RT

C
22 RT

D
26 RT

Solution
Question 3
1 / -0

Air is filled at $$60^0$$C in a vessel of open mouth. The vessel is heated to a temperature T so that $$1/4^{th}$$ part of air escapes. The value of T is :

A
$$80^0$$C

B
$$444^0$$C

C
$$333^0$$C

D
$$171^0$$C

Solution
Question 4
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$$'n'$$ moles of an ideal gas undergoes a process $$A\rightarrow B$$ as shown in the figure. The maximum temperature of the gas during the process will be :

A
$$\cfrac{3P_{0}V_{0}}{2nR}$$

B
$$\cfrac{9P_{0}V_{0}}{2nR}$$

C
$$\cfrac{9P_{0}V_{0}}{nR}$$

D
$$\cfrac{9P_{0}V_{0}}{4nR}$$

Solution

$$\begin{array}{l} y-{ y_{ 1 } }=\dfrac { { { y_{ 2 } }-{ y_{ 1 } } } }{ { { x_{ 2 } }-{ x_{ 1 } } } } \left( { x-{ x_{ 1 } } } \right) \\ P-{ P_{ 0 } }=\dfrac { { 2{ p_{ 0 } }-{ p_{ 0 } } } }{ { { v_{ 0 } }2{ v_{ 0 } } } } \left( { V-2{ V_{ 0 } } } \right) \\ =\dfrac { { -{ P_{ 0 } } } }{ { { V_{ 0 } } } } \left( { V-2{ V_{ 0 } } } \right) \\ P=\dfrac { { -{ P_{ 0 } } } }{ { { V_{ 0 } } } } V+3{ p_{ 0 } } \\ PV=\dfrac { { -{ P_{ 0 } } } }{ { { V_{ 0 } } } } V+3{ p_{ 0 } }V \\ nRT=\dfrac { { -{ P_{ 0 } } } }{ { { V_{ 0 } } } } V+3{ p_{ 0 } }V \\ T=\dfrac { 1 }{ { nR } } \left( { \dfrac { { -{ P_{ 0 } } } }{ { { V_{ 0 } } } } { V^{ 2 } }+3{ p_{ 0 } }V } \right) \\ \dfrac { { dT } }{ { dV } } =0\, \, \left( { for\, \, \max \, \, \, temperature } \right) \\ \dfrac { { -{ P_{ 0 } } } }{ { { V_{ 0 } } } } 2V+3{ p_{ 0 } }=0 \\ \dfrac { { -{ P_{ 0 } } } }{ { { V_{ 0 } } } } 2V=-3{ p_{ 0 } } \\ V=\dfrac { 3 }{ 2 } { V_{ 0 } }\, \, \, \, \left( { condtion\, \, for\, \, \max \, \, temperature } \right) \\ { T_{ \max } }=\dfrac { 1 }{ { nR } } \left( { \dfrac { { -{ P_{ 0 } } } }{ { { V_{ 0 } } } } \times \dfrac { 9 }{ 4 } V_{ 0 }^{ 2 }+3{ p_{ 0 } }\times \dfrac { 3 }{ 2 } { V_{ 0 } } } \right) \\ { T_{ \max } }=\dfrac { 1 }{ { nR } } \left( { -\dfrac { 9 }{ 4 } { P_{ 0 } }{ V_{ 0 } }+\dfrac { 9 }{ 2 } { P_{ 0 } }{ V_{ 0 } } } \right) \\ =\dfrac { 9 }{ 4 } \dfrac { { { P_{ 0 } }{ V_{ 0 } } } }{ { nR } } \end{array}$$
Question 5
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Internal energy of $$n_{1}$$ moles of hydrogen at temperature $$150\ K$$ is equal to the internal energy of $$n_{2}$$ moles of helium at temperature $$300\ K$$. The ratio of $$n_{1}/n_{2}$$ is

A
$$3:5$$

B
$$2:3$$

C
$$6:5$$

D
$$5:6$$

Solution

We have,
$$u = \dfrac{5}{2} \times {n_1} \times R \times 150 = \dfrac{3}{2} \times {n_2} \times R \times 300$$
$$ \Rightarrow \dfrac{{{n_1}}}{{{n_2}}} = \dfrac{{900}}{{750}} = \dfrac{6}{5}$$
$$\therefore$$ Option $$C$$ is correct answer.
Question 6
1 / -0

The magnetic monment of a diamagnetic atom is

A
Much greater than one

B
1

C
Between zero and one

D
Equal to zero

Solution
Question 7
1 / -0

If number of molecules of $${ H }_{ 2 }$$ are doubles than that of $${ O }_{ 2 }$$, then ratio of kinetic energy of hydrogen to that of oxygen at 300 K is

A
1.1

B
1.2

C
2.1

D
1.16

Solution
Question 8
1 / -0

Find the approximate number of molecules contained in a vessel of volume $$7$$ litres at $$0^oC$$ at $$1.3\times 10^5$$ pascals:

A
$$2.4\times 10^{23}$$

B
$$1.5\times 10^{24}$$

C
$$6\times 10^{23}$$

D
$$4.8\times 10^{23}$$

Solution
Question 9
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Where temperature of a gas, contained in closed vessel is increased by $$5C$$, its pressure increases by $$1%$$.The original temperature of the gas was approx i - mately:-

A
$$500C$$

B
$$273C$$

C
$$227C$$

D
$$50C$$

Solution
Question 10
1 / -0

An ant is walking on the horizontal surface. The number of degree of freedom of ant will be

A
$$1$$

B
$$2$$

C
$$3$$

D
$$6$$

Solution