Ideal Gas Equation from KTG

Q.

What is the unit of Van der Waals constant?

Q.

The Ideal Gas Law is applicable at

1. Low $T$, Low $P$

2. High $T$, Low $P$

3. Low $T$, High $P$

4. High $T$, High $P$

Q.

A vessel of volume $V$ contains an ideal gas at absolute temperature $T$ and pressure $P$. The gas is allowed to leak till its pressure falls to $P$. Assuming that the temperature remains constant during leakage, the number of moles of the gas that have leaked is

1. $\frac{V}{RT}(P+P^{\prime })$

2. $\frac{V}{2RT}(P+P^{\prime })$

3. $\frac{V}{RT}(P-P^{\prime })$

4. $\frac{V}{2RT}(P-P^{\prime })$

Q. An ideal gas is expanding such that $P{T}^2=constant$. The coefficient volume expansion of the gas is

1. $\frac{1}{T}$
2. $\frac{2}{T}$
3. $\frac{3}{T}$
4. $\frac{4}{T}$

Q. At constant pressure, if an ideal gas expands, the temperature increases.

1. True
2. False

Q. The quantity pV/kT represents

1. mass of the gas
2. kinetic energy of the gas
3. number of moles of the gas
4. number of molecules in the gas

Q. An ideal gas is expanding such that $P{T}^2=constant$. The coefficient volume expansion of the gas is

1. $\frac{1}{T}$
2. $\frac{2}{T}$
3. $\frac{3}{T}$
4. $\frac{4}{T}$

Q. A cylinder of fixed capacity 44.8 litre. contains a monatomic gas at standard temperature and pressure. The amount of heat required to increse the temperature of cylinder by ${10}^{\circ }$C will be. (R = universal gas constant)

1. R
2. 10R
3. 20R
4. 30R

Q. The volume of containers A and B, connected by a tube and a closed valve are $V$ and $4V$ respectively. Both the containers A and B have the same ideal gas, at pressures $5.0\times {10}^5\text{Pa}$ and $1.0\times {10}^5\text{Pa}$ and temperatures $300\text{K}$ and $400\text{K}$ respectively. The valve is opened to allow the pressure to equalise, but the temperature of each container is kept constant at its initial value. Find the common pressure in the containers.

1. $2.5\times {10}^5\text{Pa}$
2. $2.0\times {10}^5\text{Pa}$
3. $3.0\times {10}^5\text{Pa}$
4. $1.5\times {10}^5\text{Pa}$

Q.

What is ideal gas law used for?

Q. Assume that the temperature remains essentially constant in the upper part of the atmosphere. Obtain an expression for the variation of pressure in the upper atmosphere with height. (The mean molecular weight of air is $M$.)

1. $p=p_0{e}^{-\left(\frac{Mg}{RT}\right)h}$
   
   
2. $p=p_0{e}^{\left(\frac{Mg}{RT}\right)\frac{h}{2}}$
   
   
3. $p=p_0{e}^{-\left(\frac{Mg}{RT}\right)\frac{h}{2}}$
   
   
4. $p=p_0{e}^{-\left(\frac{Mg}{RT}\right)h}$
   
   

Q. Calculate the compressibility factor for a gas, if $1$ mole of it occupy $0.821\text{litre}$ at $300\text{K}$ and $50\text{atm}$.

1. $1$
2. $1.33$
3. $1.67$
4. $0.67$

Q. Two identical containers $A$ and $B$ each of volume $V_0$ are joined by a small pipe. The containers contain identical gases at temperature $T_0$ and pressure $P_0$. Container $A$ is heated to temperature $2T_0$ while maintaining $B$ at the same temperature. If the common pressure of the gas is $P$ and $n_1$ and $n_2$ are the number of moles of the gas in $A$ and $B$ respectively, then choose the correct option(s):

1. $P=\frac{4}{3}{P}_0$
2. $P=\frac{2}{3}{P}_0$
3. $n_1=\frac{2}{3}\frac{P_0{V}_0}{R{T}_0}$
4. $n_2=\frac{4}{3}\frac{P_0{V}_0}{R{T}_0}$

Q. The figure shows a cylindrical tube of radius $r$ and length $l$ fitted with a cork. The friction coefficient between the cork and the tube is $\mu$. The tube contains an ideal gas at temperature $T$ and atmospheric pressure $P_0$ . It is slowly heated and the cork pops out when the temperature is doubled. What is normal force per unit length exerted by the cork on the periphery of the tube? (Assume uniform temperature throughout the gas and mass of cork to be negligible.)

1. $\frac{P_{0}A}{2\mu r}$
2. $\frac{P_{0}A}{\mu \pi r}$
3. $\frac{P_{0}A}{4\mu \pi r}$
4. $\frac{P_{0}A}{2\mu \pi r}$

Q. Suppose an ideal gas undergoes a process given by $V{P}^3=\text{constant}$. Initial temperature and volume of the gas are $T$ and $V$ respectively. If the gas expands to $27V$, then its temperature will become

1. $T$
2. $9T$
3. $27T$
4. $\frac{T}{9}$

Q. PV=nRT is exactly true for all gases under all conditions.

1. True
2. False

Q. The volume of containers A and B, connected by a tube and a closed valve are $V$ and $4V$ respectively. Both the containers A and B have the same ideal gas, at pressures $5.0\times {10}^5\text{Pa}$ and $1.0\times {10}^5\text{Pa}$ and temperatures $300\text{K}$ and $400\text{K}$ respectively. The valve is opened to allow the pressure to equalise, but the temperature of each container is kept constant at its initial value. Find the common pressure in the containers.

1. $2.5\times {10}^5\text{Pa}$
2. $2.0\times {10}^5\text{Pa}$
3. $3.0\times {10}^5\text{Pa}$
4. $1.5\times {10}^5\text{Pa}$

Q.

Air is pumped into an automobile tyre's tube up to a pressure of 200 kPa in the morning when the air temperature is 200${}^{\circ }$C. During the day the temperature rises to 400${}^{\circ }$C and the tube expands by 2%. Calculate the pressure of the air in the tube at this temperature

1. 209 kPa

2. 285 kPa

3. 355 kPa

4. 392 kPa

Q. A given sample of an ideal gas occupies a volume $V$ at a pressure $P$ and absolute temperature $T$. The mass of each molecule of the gas is $m$. Which of the following gives the density of the gas ?

1. $P/\left(kTV\right)$
2. $mkT$
3. $P/\left(kT\right)$
4. $Pm/\left(kT\right)$

Q.

A vessel of volume $V$ contains an ideal gas at absolute temperature $T$ and pressure $P$. The gas is allowed to leak till its pressure falls to $P$. Assuming that the temperature remains constant during leakage, the number of moles of the gas that have leaked is

1. $\frac{V}{RT}(P+P^{\prime })$

2. $\frac{V}{2RT}(P+P^{\prime })$

3. $\frac{V}{RT}(P-P^{\prime })$

4. $\frac{V}{2RT}(P-P^{\prime })$

Q. Suppose an ideal gas undergoes a process given by $V{P}^3=\text{constant}$. Initial temperature and volume of the gas are $T$ and $V$ respectively. If the gas expands to $27V$, then its temperature will become

1. $T$
2. $9T$
3. $27T$
4. $\frac{T}{9}$

Q. An ideal gas is expanding such that $PT=$ constant. The coefficient of volume expansion of the gas is :

1. $\frac{1}{T}$
2. $\frac{2}{T}$
3. $\frac{3}{T}$
4. $\frac{4}{T}$

Q. The surface area of the floor of a room is $30m^2$ and the walls are 3m high. If the room temperature is ${27}^{\circ }$C and pressure is 1 atm, then find the mass of the air inside the room
[Given: Molecular weight of air = 29, 1 atm = 1.013 $\times {10}^5$ Pa]

1. 105.85 kg
2. 29 kg
3. 74.37 kg
4. 135.35 kg

Q.

560 cm³ of air is at a pressure of 76 cm of mercury. Find the pressure of air (assuming temperature remains constant), when its volume is:

840 cm³

Q.

Air is pumped into an automobile tyre's tube up to a pressure of 200 kPa in the morning when the air temperature is 200${}^{\circ }$C. During the day the temperature rises to 400${}^{\circ }$C and the tube expands by 2%. Calculate the pressure of the air in the tube at this temperature

1. 209 kPa

2. 285 kPa

3. 355 kPa

4. 392 kPa

Q. 1/2 mole oxygen gas occupies 44.8 L at temperature 273.15 K. The pressure of the oxygen gas is .

1. 0.25 atm
2. 0.5 atm
3. 4 atm

Q. An ideal gas is expanding such that $PT=$ constant. The coefficient of volume expansion of the gas is :

1. $\frac{1}{T}$
2. $\frac{2}{T}$
3. $\frac{3}{T}$
4. $\frac{4}{T}$

Q.

Two thermally insulated vessels $1$ and $2$ are filled with air at temperature ($T_1$, $T_2$), volume ($V_1$, $V_2$) and pressure ($P_1$, $P_2$) respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

1. $T_1+T_2$

2. $\frac{T_1+T_2}{2}$

3. $\frac{T_1{T}_2(P_1{V}_1+P_2{V}_2)}{P_1{V}_1{T}_2+P_2{V}_2{T}_1)}$

4. $\frac{T_1{T}_2(P_1{V}_1+P_2{V}_2)}{P_1{V}_1{T}_1+P_2{V}_2{T}_2)}$

Q. Find the ratio of specific gas constant for $H_2$ to the specific gas constant for $O_2$?

1. $16:1$
2. $1:16$
3. $1:1$
4. $1:8$

Q. A vessel of volume $2000c{m}^3$ contains 0.1 mole of $O_2$ and 0.2 mole of $C{O}_2$. If the temperature of the mixture is 300k, find its pressure.

1. $1.25\times {10}^{5}Pa$
2. $2.25\times {10}^{5}Pa$
3. $3.25\times {10}^{5}Pa$
4. $4.25\times {10}^{5}Pa$