Gas laws from KTG

Q. By what percentage should the pressure of the given mass of gas be increased so to decrease its volume by 10% at a constant temperature?

1. 5%
2. 11.1%
3. 7.2%
4. 12.5%

Q. Which one of the graph represents the behaviour of an ideal gas at constant temperature?

1. 
2. 
3. 
4. 

Q.

A 500mL Soda water is packed under 2.5 atm and CO₂ pressure at 298 K. Find out the quantity of CO₂ present in the bottle if Henry’s law constant for CO₂ in water is 1.67x108 Pa at 298 K.

Q. When temperature of an ideal gas is increased from ${27}^{\circ }\text{C}$ to ${227}^{\circ }\text{C}$ keeping its mass and pressure constant, then volume of the gas will be increased by

1. $33.33\%$
2. $66.66\%$
3. $30\%$
4. $60\%$

Q. The mean free path of nitrogen molecules at a pressure of 1.0 atm and temperature $0^{\circ }C$ is $0.8\times {10}^{-7}m$ . If the number of density of molecules is , then the molecular diameter is

1. 3.2nm
2. 2.3 mm
3. 
4. 

Q. One mole of an ideal diatomic gas is taken through the cycle as shown in the figure.
$1\to 2$ : Isochoric process
$2\to 3$ : Straight line on P-V diagram
$3\to 1$ : Isobaric process
The average molecular speed of the gas in the states $1,2$ and $3$ are in the ratio

1. $1:2:2$
2. $1:\sqrt{2}:\sqrt{2}$
3. $1:1:1$
4. $1:2:4$

Q.

Identify the correct graph between PV and T for an ideal gas.

1. a

2. b

3. c

4. d

Q. If by keeping the temperature constant, the pressure of a gas is decreased by $20\%$, then the percentage change in volume of the gas will be

1. - $20\%$
2. + $20\%$
3. + $25\%$
4. - $25\%$

Q. Two containers $A$ and $B$ contain the same ideal gas at the same temperature and pressure. If volume of container $A$ is twice the volume of container $B$, then find the ratio of gas molecules present in container $A$ to container $B$.

1. $2:1$
2. $3:2$
3. $2:3$
4. $1:2$

Q. Two containers of equal volume contain the same gas at different 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. $\frac{P_1}{T_1}+\frac{P_2}{T_2}$
2. $\frac{P_1{T}_2+P_2{T}_1}{(T_1+T_2{)}^2}$
3. $\frac{P_1{T}_1+P_2{T}_2}{(T_1+T_2{)}^2}$
4. $\frac{P_1}{2T_1}+\frac{P_2}{2T_2}$

Q. An air bubble of volume $V_0$ is released by a fish at a depth $h$ in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure $P$ above the lake. The volume of the bubble just before touching the surface will be (density of water is $\rho )$

1. $V_0$
2. $V_0\left(\frac{\rho gh}{P}\right)$
3. $\frac{V_0}{(1+\frac{\rho gh}{P})}$
4. $V_0(1+\frac{\rho gh}{P})$

Q. The time taken for a certain volume of gas to diffuse through a small hole was $2\text{min}$. Under similar conditions an equal volume of oxygen took $4\text{min}$ to pass. The molecular mass of the gas is:

1. $32.0\text{g}$
2. $16.0\text{g}$
3. $8.0\text{g}$
4. $4.0\text{g}$

Q.

A vertical cylinder of height 100 cm contains air at a constant temperature. The top is closed by a frictionless light piston. The atmospheric pressure is equal to 75 cm of mercury. Mercury is slowly poured over the piston. Find the maximum height of the mercury column that can be put on the piston.

Q. By what percentage should the pressure of a given mass of gas be increased so as to decrease its volume by 10$\%$ at a constant temperature?

1. $8.1\%$
2. $9.1\%$
3. $10.1\%$
4. $11.1\%$

Q. If speed $V$, area $A$ and force $F$ are chosen as fundamental units, then the dimension of Young's modulus will be :

1. $F{A}^2{V}^{-1}$
2. $F{A}^2{V}^{-3}$
3. $F{A}^2{V}^{-2}$
4. $F{A}^{-1}{V}^0$

Q.

What is the behavior of an ideal gas?

Q. A closed hollow insulated cylinder is filled with gas at $0^{\circ }$C and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to ${100}^{\circ }$ C .If the piston moves 5cm the length of the hollow cylinder is

1. 13.65 cm
2. 27.3 cm
3. 38.6 cm
4. 64.6 cm

Q. A pressure cooker of volume $10$ litres contains an ideal gas at atmospheric pressure ${10}^5$ Pa and temperature of $27°C$. It has a whistle which has an area of $0.1c{m}^2$ and mass of $100gm$. To what temperature should it be heated so that the whistle is just lifted up?

1. $580K$
2. $500K$
3. $470K$
4. $600K$

Q. A gas is present at a pressure of $2\text{atm}$. What should be the increase in pressure so that the volume of the gas can be decreased to $\frac{1}{4}\text{th}$ of the initial value, if the temperature is maintained constant?

1. $2\text{atm}$
2. $8\text{atm}$
3. $10\text{atm}$
4. $6\text{atm}$

Q. Mean free path for molecules of a gas is $\lambda$. If diameter of molecules is kept constant and the number density is increased to two times of its initial value, then new mean free path will be

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

Q. The rate of diffusion of two gases $A$ and $B$ is in the ratio of $1:2$ and the $B$ and $C$ in the ratio $1:8$, the rate of diffusion of $C$ with respect to $A$ is

1. $1:12$
2. $12$
3. $1:16$
4. $16$

Q.

The pressure of sodium vapor in a 1.0 L container is 10 torr at 1000 ^oC. How many atoms are in the container?

1. 9.7 × 10¹⁷

2. 7.6 × 10¹⁹

3. 4.2 × 10¹⁷

4. 9.7 × 10¹⁹

Q. By what percentage should the pressure of a given mass of a gas be increased so as to decrease its volume by $20\%$ at a constant temperature?

1. $10\%$
2. $25\%$
3. $20\%$
4. $5\%$

Q. A partition divides a container having insulated wall, into two compartments- I and II. The same gas fills the two compartments whose initial parameters are given. The partition is a conducting wall which can move freely without friction. Which of the following statements is/are correct, with reference to the final equilibrium position?

1. The pressure in the two compartments are equal
2. Volume of compartment I is $\frac{3V}{5}$
3. Volume of compartment II is $\frac{12V}{5}$
4. Final pressure in compartment I is $\frac{5P}{3}$

Q.

A gas in container A is in thermal equilibrium with identical another gas in container B. Both contain equal masses of the two gases in the respective containers. Which of the following can be true

1. 

2. 

3. 

4. 

Q.

Two gases of equal mass are in thermal equilibrium. If $P_a,P_b$ and $V_a$ and $V_b$ are their respective pressures and volumes, then which relation is true

1. 

2. 

3. 

4. 

Q. Which one of the following graph represents the behaviour of a ideal gas? Assume pressure is constant.

1. 
2. 
3. 
4. 

Q.

One mole of a perfect gas in a cylinder fitted with a piston has a pressure P, volume V and temperature T. If the temperature is increased by 1 K keeping pressure constant, the increase in volume is

1. V

2. 

3. 

4. 

Q. In a closed cylinder there are $60\text{g}Ne$ and $64\text{g}{O}_2$. If pressure of mixture of gases in cylinder is 30 bar, then partial pressure of $O_2$ in this cylinder will be (in bar).

Q. A storage tank contains $2$ moles of $Ar,3$ moles of $O_2$, $5$ moles of $N_2$. If volume of tank is $1{\text{m}}^3$, find the total pressure exerted by mixture of gases at $300\text{K}$?

1. $22000{\text{N/m}}^2$
2. $21000{\text{N/m}}^2$
3. $23500{\text{N/m}}^2$
4. $24942{\text{N/m}}^2$