Pressure vs Velocity

Q.

Pressure is exerted by a gas on the walls of the container because

1. It loses kinetic energy

2. It sticks with the walls

3. On collision with the walls there is a change in momentum

4. It is accelerated towards the walls

Q. Try to derive the relationship between pressure and the sum of velocities (say, v) of each molecule, density of the gas ($\rho$), and the total number of particles in the container (N).

1. $\frac{1}{4}\rho \Sigma \frac{v^2}{N}$
2. Common man, I don't wanna do this.
3. $\frac{1}{3}\rho \Sigma \frac{v^2}{N}$
4. $\frac{1}{2}\rho \Sigma \frac{v^2}{N}$

Q.

Assume that the temperature remains essentially constant in the upper part of the atmosphere. Obtain an expression for the variation in pressure with height in the upper atmosphere. The mean molecular weight of air is M. Assume a variable $P_O$ for the pressure at a height h = 0, where h = 0 depends on the choice of origin (could very well be at the beginning of the stratosphere, for example).

1. 

2. .

3. 

4. 

Q. The macroscopic properties of gases include its pressure (P), volume (V), its temperature (T), the quantity of the gas, which can be measured by its mass (M), or the number of gas particles (atoms/molecules; N). One of the earliest investigations on a relationship between these properties was conducted by Robert Boyle, chiefly motivated by a hunch against one of his contemporary, Toricelli's claim on how a barometer works. Boyle's set-up was as shown.

He attached a small U-tube at the end of a Toricellian tube and powered in mercury from the open end (T); as mercury rose in the closed, shorter column, the trapped air would get more and move compressed - which could only mean, that the pressure increased, and the volume decreased (these were respectively measured by the height of the mercury column, h, and a scale on the shorter column, V, for volume of the trapped air).

Which of these statements is/are correct in regard to Boyle's conclusion from the data?

1. The height difference of the two levels is directly proportional to the pressure of the trapped air

2. As the value of h increased, V monotonically decreased

3. If we blow air through the open end of T, then h would be a bad measure for the pressure of the trapped air

4. The graph of h versus the reciprocal of V is a straight line

Q.

The Bat Life: To monitor the pressure of helium in the canister, Batman had placed 2 sensors which sense pressure and temperature at points $P_{1}and{P}_2$. When the piston was in motion, Batman's suit registered an error in the canister. When he analysed the error back in the Batcave he noticed that the pressure at points $P_{1}and{P}_2$ were different. Which amongst the following statements is true?

1. its a trick of the JOKER.
2. none of the above

3. The sensors which detect the pressure at points $P_{1}and{P}_2$ are faulty. A gas confined within a single boundary cannot have twovalues of pressure

4. The sensors need not necessarily be faulty, as the gas is not in equilibrium.

Q.

An air bubble of radius 2.0 mm is formed at the bottom of a 3.3 m deep river. Calculate the radius of the bubble as it comes to the surface. Atmospheric pressure $=1.0\times {10}^5$ Pa and density of water $=1000kg{m}^{-3}$

1. 2.2mm

2. 1.8mm

3. 2.8mm

4. 2mm

Q.

Two containers of equal volume contain the same gas at pressures $P_1$ and $P_2$ and absolute temperatures $T_1$ and $T_2$ respectively. On joining the vessels, the gas reaches a common pressure P and common temperature T. The ratio $\frac{P}{T}$ is equal to

1. 

2. 

3. 

4. 

Q.

The Bat Life: What can be said with 100% confidence about the temperatures at point $P_{1}and{P}_2$?

1. .

2. >

3. <

4. 

Q.

At absolute zero temperature, pressure of a gas will be

1. Zero

2. One atmospheric pressure

3. 

4. 

Q.

If the mean free path of atoms is doubled then the pressure (P) of gas will become

1. P

2. P/4

3. P/8

4. P/2