Real Gas Equation

Q. Which of the following gases can be most easily liquified? Given, the value of $a$ in van der Waals equation for $N{H}_3=4.17,C{O}_2=3.59,S{O}_2=6.71\&C{l}_2=6.49$

1. $N{H}_3$
2. $C{l}_2$
3. $S{O}_2$
4. $C{O}_2$

Q. The Bat Life: Batman is undercover, and to prevent anyone from recognizing his voice (or Bruce Wayne's) he inhales a very dilute Helium gas (search YouTube for "voice after helium” to see the effects). The helium is stored ina cylindrical chamber as shown.

During a fight one of the steel balls gets dislodged. What will happen to the piston?

1. It will move down

2. It will move up

3. Not enough information, only Batman will know

4. It will remain in the same place

Q.

The work done by a gas when it undergoes a state change from 1 $\to$ 2 isothermally is

1. 

2. 

3. 

4. 

Q. At higher pressure, which one of the following is correct about volume of the gases?

1. $V_{real}>V_{ideal}$
2. $V_{real}<V_{ideal}$
3. $V_{real}=V_{ideal}$
4. None of these

Q. $1$ mole of real gas $(a=1.4)$ occupies a volume of $0.1\text{L}$ at $300\text{K}$, then what will be the pressure of gas?

1. $2460\text{atm}$
2. $2320\text{atm}$
3. $106\text{atm}$
4. $212\text{atm}$

Q. The equation of state of a gas is given by $P(V-b)=nRT$. If $1\text{mole}$ of a gas is isothermally expanded from volume $V$ and $2V$, the work done during the process is

1. $\text{RT ln}\left(\frac{2V-b}{V-b}\right)$
2. $\text{RT ln}\left(\frac{V-b}{V}\right)$
3. $\text{RT ln}\left(\frac{V-b}{2V-b}\right)$
4. $\text{RT ln}\left(\frac{V}{V-b}\right)$

Q. For one mole of a van der Waals gas for which $b=0$ and $T=300\text{K}$, the $PV\text{vs}\frac{1}{V}$ plot is shown below. The value of the van der Waals constant $a$ (in ${\text{atm L mol}}^{-2}$) is:

1. $1.0$
2. $4.5$
3. $1.5$
4. $3.0$

Q. In Van der Waal's equation of state of the gas, the constant ${}^{\prime }{b}^{\prime }$ is a measure of:

1. intermolecular collisions per unit volume.
2. intermolecular attraction.
3. volume occupied by molecules.
4. intermolecular repulsions.

Q. Under which of the following condition is the law $PV=nRT$ obeyed most closely by a real gas?

1. High pressure and high temperature
2. Low pressure and low temperature
3. Low pressure and high temperature
4. High pressure and low temperature

Q. Pressure exerted by $1\text{mole}$ of methane in $0.25\text{litre}$ container at $300\text{K}$ using Van der Waal's equations?
Given $a=2.25{\text{atm - L}}^2/{\text{mol}}^2$
$b=0.05\text{L/mol}$

1. $86\text{atm}$
2. $87.15\text{atm}$
3. $100\text{atm}$
4. $50\text{atm}$

Q. Explain why
(a) To keep a piece of paper horizontal, you should blow over, not under, it .
(b) When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingers.
(c) The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection.
(d) A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel.
(e) A spinning cricket ball in air does not follow a parabolic trajectory.

Q. $1$ mole of real gas $(a=1.4)$ occupies a volume of $0.1\text{L}$ at $300\text{K}$, then what will be the pressure of gas?

1. $2460\text{atm}$
2. $2320\text{atm}$
3. $106\text{atm}$
4. $212\text{atm}$