IIT JEE & NEET Question Bank with Solution: Kinetic Theory Of Gases : Physics Entrance Exam

Q.1. If k is the Boltzmann constant , the average kinetic energy of a gas molecule at absolute temperature T is

A) k T/2

B) 3 k T/4

C) k T

D) 3 k T/2

Q.2. At room temperature (27 $degree$ C ) the rms speed of the molecules of a certain diatomic gas is found to be 1920 ms $blank to the power of negative 1 end exponent$ .The gas is

A) H $blank subscript 2$

B) F $blank subscript 2$

C) O $blank subscript 2$

D) CI $blank subscript 2$

Explanation-

We know that $ϑ subscript r m s end subscript space equals space square root of fraction numerator 3 R T over denominator M end fraction end root$ which gives

$M equals fraction numerator 3 space R T over denominator ϑ squared subscript r m s end subscript end fraction equals fraction numerator 3 cross times 8.3 cross times 300 over denominator open parentheses 1920 close parentheses squared end fraction space space space equals space 2 cross times 10 to the power of negative 3 end exponent space k g space equals space 2 space g$

Since M = 2 , the gas is hydrogen .

Q.3. If a g as has f degrees of freedom, the ratio $C subscript p divided by C subscript v$ of the gas is

A) $fraction numerator 1 plus f over denominator 2 end fraction$

B) $1 plus f over 2$

C) $1 half plus f$

D) $1 plus 2 over f$

Explanation-

We know that $C subscript ϑ$ = no . of degress of freedom x molar gas constant / 2 or $C subscript ϑ equals f R divided by 2. space A l s o space C subscript p minus C subscript ϑ space equals space R T h e r e f o r e C subscript p over C subscript ϑ space R over C subscript ϑ plus 1 equals fraction numerator 2 R over denominator f space R end fraction plus 1 equals 2 over f plus 1$

Q.4. Two ideal gases at absolute temperature T $blank subscript 1$ and T $blank subscript 2$ are mixed . There is no loss of energy in this process . If n $blank subscript 1$ and n $blank subscript 2$ are the respective number of molecules of the gases , the temperature of the mixture will be

A) $fraction numerator n subscript 1 T subscript 1 space plus space n subscript 2 T subscript 2 over denominator n subscript 1 plus n subscript 2 end fraction$

B) $fraction numerator n subscript 2 T subscript 1 plus n subscript 1 T subscript 2 over denominator n subscript 1 plus n subscript 2 end fraction$

C) $T subscript 1 plus n subscript 2 over n subscript 1 T subscript 2$

D) $T subscript 2 plus n subscript 1 over n subscript 2 T subscript 1$

Explanation-

$fraction numerator n subscript 1 T subscript 1 space plus space n subscript 2 T subscript 2 over denominator n subscript 1 plus n subscript 2 end fraction$

Q.5. Four molecules of a gas have speeds 1,2,3 and 4 km $s to the power of negative 1 end exponent$ . The value of the root mean square speed of the gas molecule is

A) $1 half space square root of 15 space end root space k m space s to the power of negative 1 end exponent$

B) $1 half square root of 10 space k m space s to the power of negative 1 end exponent$

C) $2.5 space k m space s to the power of negative 1 end exponent$

D) $square root of 15 divided by 2 end root space k m space s to the power of negative 1 end exponent$

Explanation-

The rms speed = $open square brackets fraction numerator 1 squared plus 2 squared plus 3 squared plus 4 squared over denominator 4 end fraction close square brackets to the power of 1 divided by 2 end exponent equals space square root of 15 over 2 end root space k m s to the power of negative 1 end exponent$

Q.6. The average kinetic energy of a molecule of a gas at absolute temperature T is proportional to

A) 1/T

B) $square root of T$

C) T

D) T $blank squared$

Explanation-

The average kinetic energy of a molecule of a gas at absolute temperature T is given by $straight E space equals space 3 over 2 space kT$ .

Q.7. The root mean square speed of the molecules of a gas at absolute temperature T is proportional to

A) 1/T

B) $square root of T$

C) T

D) T $blank squared$

Explanation-

The root mean square speed of the molecules of a gas is given by $straight ϑ subscript rms space end subscript equals space square root of fraction numerator 3 space kT over denominator straight m end fraction end root$ .

Q.8. $E subscript 0$ and $E subscript h$ respectively represent the average kinetic energy of a molecule of oxygen and hydrogen. If the two gases are at the same temperature , which of the following statements is true ?

A) $E subscript 0$ > $E subscript h$

B) $E subscript 0$ = $E subscript h$

C) $E subscript 0$ < $E subscript h$

D) Nothing can be said about the magnitude of $E subscript 0$ and $E subscript h$ as the information given is insufficient

Explanation-

The average kinetic energy of molecule = $1 half$ kT which is independent of the molecular mass .

Q.9. The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K , the root mean square speed of the gas molecules is v , then at 480 K it will be

A) 4 v

B) 2 v

C) $v over 2$

D) $v over 4$

Explanation-

$ϑ subscript r m s end subscript equals square root of fraction numerator 3 R T over denominator M end fraction end root space o r space ϑ subscript r m s end subscript proportional to square root of T$ .

Q.10. A vessel contains 1 mole of O $blank subscript 2$ gas ( molar mass 32 ) at a temperature T . The pressure of the gas is P . An identical vessel containing one mole of He gas ( molar mass 4 ) at a temperature 2 T has a pressure of

A) $p over 8$

B) P

C) 2 P

D) 8 P

Explanation-

For a gas , PV = nRT . Hence

( P ) $open parentheses straight P close parentheses o subscript 2 equals fraction numerator open parentheses 1 space m o l e close parentheses space R T over denominator V end fraction a n d space left parenthesis P right parenthesis subscript H e end subscript equals fraction numerator open parentheses 1 space m o l e close parentheses R open parentheses 2 T close parentheses over denominator V end fraction therefore fraction numerator open parentheses P close parentheses subscript H e end subscript over denominator open parentheses P close parentheses o subscript 2 end fraction space equals 2 space o r space left parenthesis P right parenthesis subscript H e end subscript equals 2 open parentheses P close parentheses o subscript 2$

IIT JEE & NEET Question Bank with Solution

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Thursday, August 19, 2021

Kinetic Theory Of Gases : Physics Entrance Exam

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