Ideal Gas Equation from KTG

Q. An ideal gas is expanding such that $P{T}^3=$ constant. The coefficient of volume expansion of the gas is:

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

Q. A partition divides a container having insulated walls into two compartments I and II as shown in the figure. 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 statement(s) is /are correct with reference to the final equilibrium position?

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

Q. Air is filled at ${60}^{\circ }\text{C}$ in a vessel of open mouth. The vessel is heated to a temperature $T$, so that $\frac{1}{4}\text{th}$ part of the air escapes. Assuming the volume of the vessel remains constant, the value of $T$ is

1. ${44}^{\circ }\text{C}$
2. ${333}^{\circ }\text{C}$
3. ${171}^{\circ }\text{C}$
4. ${80}^{\circ }\text{C}$

Q.

A gas is found to have the formula ${\left(CO\right)}_X$ if its vapor density is 70. Find the value of X.

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. 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 heights of mercury surfaces in the two arms of the manometer shown in figure (13-E1) are 2 cm and 8 cm. Atmospheric pressure = $1.01\times {10}^{5}N{m}^{-}2$. Find

(a) the pressure of the gas in the cylinder and

(b) the pressure of mercury at the bottom of the U tube.

Q.

An electric bulb of volume 250 cc was sealed during manufacturing at a pressure of ${10}^{-3}$ mm of mercury at ${27}^0$C. Compute the number of air molecules contained in the bulb. Avogadro constant= 6 $\times$ ${10}^{23}$ $mo{l}^{-1}$, density of mercury = 13600 kg $m^{-3}$and g = 10 m $s^{-2}$.

Q.

In Freundlich adsorption isotherm at moderate pressure, the extent of adsorption (x/m) is directly proportional to P^x. The value of x is:

1. ∞

2. zero

3. 1

4. 1/n

Q.

The density Of an ideal gas is 1.25 $\times {10}^{-3}$ g cm at STP. Calculate the molecular weight of the gas.

Q. A gas is filled in a vessel at 27C . To what temperature should it be heated in order that 1/3rd of the gas may escape out of the vessel ?

Q.

Equal masses of air are sealed in two vessels, one of volume $V_0$ and the other of volume 2$V_0$. If the first vessel is maintained at a temperature 300 K and the other at 600 K, find the ratio of the pressures in the two vessels.

Q.

If the absolute temperature of a gas is doubled then the volume of a gas is_______.

Q. Water flows in a horizontal tube (see figure). The pressure of water changes by $700{\text{Nm}}^{-2}$ between $A$ and $B$, where the areas of cross-section are $40{\text{cm}}^2\text{and}20{\text{cm}}^2$, respectively. Find the rate of flow of water through the tube. (density of water $=1000{\text{kgm}}^{-3}$)

1. $3020{\text{cm}}^3/\text{s}$
2. $2720{\text{cm}}^3/\text{s}$
3. $2420{\text{cm}}^3/\text{s}$
4. $1810{\text{cm}}^3/\text{s}$

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. 

2. 

3. 

4. 

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

Q. $2$ moles of a monatomic ideal gas is enclosed in an adiabatic fixed vertical cylinder fitted with a smooth, light and adiabatic piston. The piston is connected to a vertical spring of spring constant $200\text{N/m}$ as shown in figure. The area of cross-section of the cylinder is $20{\text{cm}}^2$. Initially, the spring is at its natural length and temperature of the gas is $300\text{K}$. The atmospheric pressure is $100\text{kPa}$. The gas is heated slowly for some time by means of an electric heater so as to move the piston up (slowly) by $10\text{cm}$. Then:

1. Work done by the gas is $21\text{J}$.
2. Work done on the gas is $21\text{J}$.
3. Heat supplied by the heater is $772\text{J}$.
4. Heat supplied by the heater is $793\text{J}$.

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. $4.25\times {10}^{5}Pa$

Q. If N is Avogadro's number, the number of molecules in 6 g of hydrogen at NTP is

Q. The temperature $T$ of one mole of an ideal gas varies with its volume $V$ as $T=-\alpha V^3+\beta V^2$, where $\alpha$ and $\beta$ are positive constants. The maximum pressure of the gas during this process is

1. $\frac{\alpha \beta }{2R}$
2. $\frac{{\beta }^{2}R}{4\alpha }$
3. $\frac{(\alpha +\beta )R}{2{\beta }^2}$
4. $\frac{{\alpha }^{2}R}{2\beta }$

Q. A leakage begins in water tank at position $\text{P}$ as shown in the figure. The initial gauge pressure (pressure above that of the atmosphere) at $\text{P}$ was $5\times {10}^5{\text{N/m}}^2$. If the density of water is $1000{\text{kg/m}}^3$, the initial velocity with which water gushes out is approximately.

1. $3.2\text{m/s}$
2. $32\text{m/s}$
3. $28\text{m/s}$
4. $2.8\text{m/s}$

Q.

A glass tube, sealed at both ends, is 100 cm long. It lies horizontally with the middle 10 cm containing mercury. The two ends of the tube contain air at ${27}^0$C and at a pressure 76 cm of mercury. The air column on one side is maintained at $0^0$C and the other side is maintained at ${127}^0$C. Calculate the length of the air column on the cooler side. Neglect the changes in the volume of mercury and of the glass.

Q.

Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 m³ at a temperature of 27 °C and 1 atm pressure.

Q.

A container of volume 50 cc contains air (mean molecular weight = 28.8 g) and is open to atmosphere where the pressure is 100 kPa. The container is kept in a bath containing melting ice ($0^0$C). (a) Find the mass of the air in the container when thermal equilibrium is reached. (b) The container is now placed in another bath containing boiling water (${100}^0$C). Find the mass of air in the container. (c) The container is now closed and placed in the melting-ice bath. Find the pressure of the air when thermal equilibrium is reached.

Q. A gas taken through the cycle $A\to B\to C\to A$, as shown, what is the net work done by the gas?

1. $-2000\text{J}$
2. $2000\text{J}$
3. $1000\text{J}$
4. $0\text{J}$

Q. One mole of an ideal gas at initial temperature $T$, undergoes a quasi -static process, during which the volume $V$ is doubled. During the process, the internal energy $U$ varies with volume as $U=a{V}^3$, where $a$ is a constant. The work done during this process is $pRT$ where $p$ is

Q. The rectangular box shown in Fig has a partition which can slide without friction along the length of the box. Initially, each of the two chambers of the box has one mole of a mono-atomic ideal gas $(\gamma =5/3)$ at a pressure $P_0$, volume $V_0$ and temperature $T_0$. The chamber on the left is slowly heated by an electric heater. The walls of the box and the partition are thermally insulated. Heat loss through the lead wires of the heater is negligible. The gas in the left chamber expands pushing the partition, until the final pressure in both chambers becomes $243P_0/32$. Determine the work done by the gas in the right chamber.
[Take $R=8.3\text{J/K mol}$]

1. $15.5T_0$
2. $-25.8T_0$
3. $-15.5T_0$
4. $25.8T_0$

Q. A gas has a density of $3\text{g/L}$ at S.T.P. What is its molar mass?

1. $67.2\text{g}$
2. $40\text{g}$
3. $20.4\text{g}$
4. $10\text{g}$

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

1. False
2. True

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. $\frac{T}{9}$