Real Gas Equation

Q.

What is a real life example of ideal gas law?

Q.

What are the four principles of kinetic molecular theory?

Q. A sample of gas with $\gamma =1.5$ is taken through an adiabiatic process in which the volume is compressed from $1200{\text{cm}}^3$ to $300{\text{cm}}^3$. if the initial pressure is $200\text{kPa}$. The absolute value of the workdone by the gas in the process
$\text{J}$.

Q. Assertion: The compressibility factor for $H_2$​ and $He$ is $(1+\frac{Pb}{RT})$
Reason: The compressibility factor for $H_2$​ and $He$ can be derived from Van der Waal's equation.

1. Both assertion and reason are correct and reason is the correct explanation for assertion.
2. Both assertion and reason are correct but reason is not the correct explanation for assertion.
3. Assertion is incorrect but reason is correct.
4. Assertion is correct but reason is incorrect.

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 pressure of an ideal gas varies with volume as $P=\alpha V$, where $\alpha$ is a constant. One mole of the gas is allowed to undergo expansion such that its volume becomes $\text{m}$ times its initial volume. The work done by the gas in the process is

1. $\frac{\alpha V^2}{2}(m^2-1)$
2. $\frac{\alpha }{2}(m^2-1)$
3. $\frac{{\alpha }^2{V}^2}{2}(m^2-1)$
4. $\frac{\alpha V}{2}(m^2-1)$

Q. At relatively high pressure, van der Waals equation reduces to

1. $PV=RT$
2. $PV=RT+\frac{q}{V}$
3. $PV=RT+Pb$
4. $PV=RT-\frac{a}{V^2}$

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. $212\text{atm}$
4. $106\text{atm}$

Q. Assertion: The compressibility factor for $H_2$​ and $He$ is $(1+\frac{Pb}{RT})$
Reason: The compressibility factor for $H_2$​ and $He$ can be derived from Van der Waal's equation.

1. Both assertion and reason are correct and reason is the correct explanation for assertion.
2. Both assertion and reason are correct but reason is not the correct explanation for assertion.
3. Assertion is correct but reason is incorrect.
4. Assertion is incorrect but reason is correct.

Q. The value of ${}^{\prime }{a}^{\prime }$ in Van der Waal's equation for the gases $O_2,N_2,N{H}_3$ and $C{H}_4$ are $1.35,1.38,4.16$ and $2.25$ respectively. The gas which can most easily be liquified is

1. $O_2$
2. $N_2$
3. $C{H}_4$
4. $N{H}_3$

Q. Compressibility factor $\left(Z\right)$ for $N_2$ at $-{23}^{\circ }\text{C}$ and $821\text{atm}$ is $1.25$. Calculate the number of moles of nitrogen gas needed to fill a gas cylinder of $100\text{litre}$ capacity under given condition.

1. $2060$
2. $3000$
3. $3200$
4. $2500$

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. $n$ moles of a perfect gas undergoes a cyclic process $ABCA$ (see figure) consisting of the following processes -

$A\to B$ : Isothermal expansion at temperature $T$ so that the volume is doubled from $V_1$ to $V_2$ and pressure changes from $P_1$ to $P_2$.

$B\to C$ : Isobaric compression at pressure $P_2$ to initial volume $V_1$.

$C\to A$ : Isochoric change, leading to change of pressure from $P_2$ to $P_1$.

Total work done in the complete cycle $ABCA$ is :

1. $0$
2. $nRT(\ln 2+\frac{1}{2})$
3. $nRT\left(\ln 2\right)$
4. $nRT(\ln 2-\frac{1}{2})$

Q. At S.T.P, the volume of $1\text{mole}$ of gas is measured to be $25\text{litres}$ then nature of gas and type of force dominating are

1. Real gas with -ve deviation, repulsive force.
2. Real gas with + ve deviation, repulsive force.
3. Real gas with -ve deviation, attractive force.
4. Real gas with +ve deviation, attractive force.

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.

Which amongst the following graphs represents the V-T graph shown in the figure?

1. 

2. 

3. 

4. 

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

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

Q.

The perfect gas equation is $\mathrm{PV}=\mathrm{nRT}$ where $\text{n}$ is the

1. Number of moles

2. Amount of gas

3. Volume of gas

4. Pressure of gas

Q. At relatively high pressure, van der Waals equation reduces to

1. $PV=RT$
2. $PV=RT+\frac{q}{V}$
3. $PV=RT+Pb$
4. $PV=RT-\frac{a}{V^2}$

Q. Carnot cycle efficiency depends upon

1. Properties of gas used in engine
2. Temperature range in which engine is operated
3. Temperature of surrounding
4. Insulating property of material of engine

Q. Match the Van der Waal's for one $\text{mole}$ of gas given in column $B$ to the conditions in column $A$.
$$\begin{array}{cccc}& \text{Column 1}& & \text{Column 2}\\ A& \text{At low pressure}& i& P(V-b)=RT\\ B& \text{At high pressure}& ii& (P+\frac{a}{V^2})V=RT\\ C& \text{At low pressure and high temperature}& iii& PV=RT\\ D& \text{At room temperature and pressure}& iv& (P+\frac{a}{V^2})(V-b)=RT\end{array}$$

1. $A-\left(i\right);B-\left(ii\right);C-\left(iii\right);D-\left(iv\right)$
2. $A-\left(ii\right);B-\left(i\right);C-\left(iii\right);D-\left(iv\right)$
3. $A-\left(iv\right);B-\left(iii\right);C-\left(ii\right);D-\left(i\right)$
4. $A-\left(iii\right);B-\left(ii\right);C-\left(i\right);D-\left(iv\right)$

Q. Read the given statements and decide which is/are correct on the basis of kinetic theory of gases

1. Energy of one molecule at absolute temperature is zero
2. rms speeds of different gases are same at same temperature
3. For one gram of all ideal gas kinetic energy is same at same temperature
4. For one mole of all ideal gases mean kinetic energy is same at same temperature

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

Q. A container is divided into two chambers by a partition. The volume of the first chamber is $4.5\text{L}$ and the second chamber is $5.5\text{L}$. The first chamber contains $3.0\text{mol}$ of gas at pressure $2.0\text{atm}$ and the second chamber contain $4.0\text{mol}$ of identical gas at pressure $3.0\text{atm}$. After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is $x\times {10}^{-1}\text{atm}$. Value of $x$ is _______. $($up to two significant figures$)$

Q.

The figure here shows four paths on a p-V diagrams along which as gas can be taken from state i to state f. Rank the paths according to -

1.the change $\Delta E_{int}$ in the internal energy of the gas.

1. 1 > 2 > 3 > 4

2. 1 = 2 = 3 = 4

3. 4 > 3 > 2 > 1

4. Need more information

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. A thermodynamic cycle $xyz$ is shown on a $V-T$ diagram.


The $P-V$ digram that best describe this cycle is : (diagrams are schematic and not to scale)

1. 
2. 
3. 
4. 

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

1. volume occupied by molecules.
2. intermolecular collisions per unit volume.
3. intermolecular attraction.
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. Assertion :Real gases behave as ideal gases most closely at low pressure and high temperature. Reason: Intermolecular force between ideal gas molecules is assumed to be zero.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct