Kinetic Theory Test

Result

Kinetic Theory Test - 58

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Weekly Quiz Competition

Question 1
1 / -0

When an ideal monoatomic gas is heated zt constant pressure , which of the following may be true

A
$$\dfrac {dU}{dQ} = \frac {3}{5}$$

B
$$\dfrac {dW}{dQ} = \frac {2]}{5}$$

C
$$\dfrac {dU}{dQ} = \frac {4}{5}$$

D
$$dW + dU = dQ $$

Solution

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Question 2
1 / -0

The kinetic energy for 14 grams of nitrogen gas at $$127$$ is nearly (mol. mass of nitrogen $$= 28$$ and gas constant $$=8.31{ JK }_{ -1 }{ mol }_{ -1 }$$ )

A
$$1.0J$$

B
$$4.15J$$

C
$$2493J$$

D
$$3.3J$$
Question 3
1 / -0

$$2$$ grams of mono atomic gas occupies a volume of $$2$$ litres at a pressure of $$8.3 \times 10^5$$ Pa and $$127^0C$$. Find the molecular weight of the gas.

A
$$2$$ grams/mole

B
$$16$$ grams/mole

C
$$4$$ grams/mole

D
$$32$$ grams/mole

Solution
Question 4
1 / -0

Two moles of an ideal gas X occupying a volume V excert a pressure P. The same pressure is excert by one mole of another gas Y occupying a volume 2V. (if the molecular weight of Y is 16 times the molecular weight of X), find the ratio of the 'rms' speed of the molecular of X and Y.

A
$$2$$

B
$$4$$

C
$$\frac { 1 }{ 2 } $$

D
$$\sqrt { 2 } $$

Solution

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Question 5
1 / -0

The maximum speed of the molecules of a gas in a vessel is $$400\ m/s$$. If half of the gas leaks out, at constant temperature, the $$rms$$ speed of the remaining molecules will be-

A
$$800\ m/s$$

B
$$400\sqrt2\ m/s$$

C
$$400\ m/s$$

D
$$200\ m/s$$

Solution

Given,
$$v_{rms}=400m/s$$
The RMS speed of the molecules will be
$$v_{rms}=\sqrt{\dfrac{3RT}{M}}$$. . . . . .(1)
where $$R=$$ universal gas constant
$$T=$$ temperature
$$M=$$ molecular weight
The RMS speed does not depend on the quantity of the gas. For a given gas and the temperature, it remains constant.
So, the RMS speed of the remaining molecules is $$400m/s$$.
The correct option is C.
Question 6
1 / -0

Heat is added to an ideal gas, and the gas expands. In such a process the temperature

A
must always increase

B
will remain the same if the work done equals the heat added

C
must always decrease

D
will remains the same If change in internal energy equals the heat added.

Solution

Heat is added to an ideal gas, and the gas expands must always increases.
Hence Option $$A$$ is correct.
Question 7
1 / -0

The rms speed of $${ N }_{ 2 }$$ molecular at STP (P=1 tm; T=$${ 0 }^{ 0 }C$$) is.....
(the density of $${ N }_{ 2 }$$ in these conditions is 1.25 $${ kg/m }^{ 3 }$$

A
493 m/s

B
390 m/s

C
290 m/s

D
590 m/s

Solution

Given,
$$P=1.013\times 10^5Pa$$
$$T=273.15 K$$
$$\rho =1.25kg/m^3$$
The rms speed of $$N_2$$ molecules is given by
$$V_{rms}=\sqrt{\dfrac{3RT}{M}}=\sqrt{\dfrac{3P}{\rho}}$$
$$V_{rms}=\sqrt{\dfrac{3P}{\rho}}$$
$$V_{rms}=\sqrt{\dfrac{3\times 1.013\times 10^5}{1.25}}=493 m/s$$
The correct option is A.
Question 8
1 / -0

On increasing temperature of the reacting system by $$10$$ degrees the rate of reaction almost doubles. The most appropriate reason for this is

A
collision frequency increases

B
activation energy decreases by increases in temperatuer

C
the fraction of molecules having energy equal to threshold energy or more increase

D
the value of threshold energy decreases

Solution
Question 9
1 / -0

Two spherical vessel of equal volumes, are connected by a narrow tube. The apparatus contains an ideal gas at one atmosphere and 300K. Now if one vessel is immersed in a bath of constant temperature 600 K and the other in a bath of constant temperature 300 K. Then the common pressure will be

A
$$1 atm$$

B
$$4/5 atm$$

C
$$4/3 atm$$

D
$$3/4 atm$$
Question 10
1 / -0

A real gas most closely approaches the behaviour of an ideal gas at :

A
15 atm and 200 K

B
1 atm and 273 K

C
0.5 atm and 500 K

D
15 atm and 500 K

Solution