1. In a vessel, the gas is at a pressure P. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be

1. 1. 4P

   
   
   

   2. 2P

   
   
   

   3. P

   
   
   

   4. P/2

   
   
   

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1. View Hint View Answer Discuss in Forum

   ∵ P =	1		mn	Vrms²
   	3		V

   
   When mass is halved and speed is doubled then
   

   Resultant pressure, Pt =	1	×	m	×	n	(2vrms)² = 2P;
   	3		2		V

   
   

   Correct Option: A

   ∵ P =	1		mn	Vrms²
   	3		V

   
   When mass is halved and speed is doubled then
   

   Resultant pressure, Pt =	1	×	m	×	n	(2vrms)² = 2P;
   	3		2		V

   
   

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2. At constant volume, temperature is increased then

1. 1. collision on walls will be less

   
   
   

   2. number of collisions per unit time will increase

   
   
   

   3. collisions will be in straight lines

   
   
   

   4. collisions will not change.

   
   
   

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1. View Hint View Answer Discuss in Forum

   As the temperature increases, the average velocity increases. So, the collisions are faster.

   Correct Option: B

   As the temperature increases, the average velocity increases. So, the collisions are faster.

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3. The molecules of a given mass of a gas have r.m.s. velocity of 200 ms^–1 at 27°C and 1.0 × 105 Nm^–2 pressure. When the temperature and pressure of the gas are respectively, 127°C and 0.05 × 10⁵ Nm^–2, the r.m.s. velocity of its molecules in ms^–1 is :

1. 1. 100√2

   
   
   

   2. 400

      √3

   
   
   

   3. 100√2

      3

   
   
   

   4. 100

      3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here v₁ = 200 m/s;
   temperature T₁ = 27°C = 27 + 273 = 300 k
   temperature T₂ = 127° C = 127 + 273 = 400 k, V = ?
   R.M.S. Velocity, V ∝ √T
   

   ⇒	v	= √	400
   	200		300

   
   

   ⇒ v =	200 × 2	m/s ⇒ v =	400	m/s
   	√3		√3

   
   

   Correct Option: B

   Here v₁ = 200 m/s;
   temperature T₁ = 27°C = 27 + 273 = 300 k
   temperature T₂ = 127° C = 127 + 273 = 400 k, V = ?
   R.M.S. Velocity, V ∝ √T
   

   ⇒	v	= √	400
   	200		300

   
   

   ⇒ v =	200 × 2	m/s ⇒ v =	400	m/s
   	√3		√3

   
   

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4. The equation of state, corresponding to 8g of O₂ is

1. 1. PV = 8 RT

   
   
   

   2. PV = RT /4

   
   
   

   3. PV = RT

   
   
   

   4. PV = RT/2

   
   
   

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1. View Hint View Answer Discuss in Forum

   8g of oxygen is equivalent to (1/4) mole.
   

   So, PV =	1	RT
   	4

   Correct Option: B

   8g of oxygen is equivalent to (1/4) mole.
   

   So, PV =	1	RT
   	4

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5. At 0 K, which of the following properties of a gas will be zero?

1. 1. Kinetic energy

   
   
   

   2. Potential energy

   
   
   

   3. Density

   
   
   

   4. Mass

   
   
   

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1. View Hint View Answer Discuss in Forum

   At 0 K, molecular motion stops. Hence, kinetic energy of molecules becomes zero.

   Correct Option: A

   At 0 K, molecular motion stops. Hence, kinetic energy of molecules becomes zero.

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