Gas Laws & Ideal Gas Equation

At constant temperature, the volume of a gas is to be decreased by 4%. The pressure must be increased by

A balloon contains $500$ m$^{3}$ of He at $27^\circ$C and $1$ atmospheric pressure. Then, volume of He at $-3^\circ$C and $0.5$ atmospheric pressure will be

The pressure of a given mass of a gas is decreased by $20\%$ at constant temperature, then its volume will

An ideal gas is heated from $27^\circ$C to $627^\circ$C at constant pressure. If initial volume of gas is $4$ m$^{3}$, then the new volume of the gas will be

A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature $50^\circ\text{C}$. The gas is now heated to double its temperature. The modified pressure is ______ Pa.

The gas in a vessel is subjected to a pressure of $20$ atm. at $27^\circ$ C. Now half of the gas is released from the vessel and the temperature is raised by $50^\circ$ C. The pressure of a gas in a vessel is nearly

At a pressure P and temperature T, 7 gram of oxygen occupies a volume V. The equation of state will be (Molecular weight of Oxygen $= 32$)

A vessel has $6$ gram of hydrogen at pressure $P$ and temperature $500$ K. A small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is $\frac{P}{2}$ and the temperature falls to $300$ K?

When 300 J of heat given to an ideal gas with $C_p = \frac{7}{2}R$ its temperature raises from $20^\circ\text{C}$ to $50^\circ\text{C}$ keeping its volume constant. The mass of the gas is (approximately) ______ g. $(R = 8.314\text{ J/mol.K})$

An insulated cylinder of volume $60\text{ cm}^{3}$ is filled with a gas at $27^\circ\text{C}$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20\text{ cm}^{3}$ while allowing the temperature to rise to $77^\circ\text{C}$. The final pressure is ______ atmospheric pressure.

At $10^\circ$C, the value of density of a fixed mass of a gas (ideal) divided by its pressure is $x$. At $110^\circ$C this ratio is

Gas at pressure P, temperature T, and volume V is filled in jar A. Another jar B is filled with gas having parameters $2P, \frac{V}{4}, 2T$. The ratio of number of molecules of jar B to those of jar A is

An ideal gas at pressure 'P' and temperature 'T' is enclosed in a vessel of volume 'V'. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to $P'$. Assuming that the temperature of the gas remains constant during the leakage, the number of moles of the gas that have leaked is

An air bubble of volume $2.9\text{ cm}^{3}$ rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is $17^\circ\text{C}$. The volume of the bubble when it reaches the surface, where the water temperature is $27^\circ\text{C}$, is $\underline{\qquad}\ \text{cm}^{3}$.

( $g = 10\text{ m/s}^{2}$, density of water $= 10^{3}\text{ kg/m}^{3}$, and 1 atm pressure is $10^{5}\text{ Pa}$)

A mixture of carbon dioxide and oxygen has volume 8310 cm3, temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are ______.

(Assume both carbon dioxide and oxygen gases behave like ideal gases) [R = 8.31 J/mol K]

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K. Keeping the temperature of one vessel constant at 400 K the second vessel temperature is raised to 500 K. The final pressure in the vessels is ______ kPa.

A balloon is filled at $27^\circ\text{C}$ and 1 atmospheric pressure by volume $500\text{ m}^{3}$ helium gas. At $-3^\circ\text{C}$ and 0.5 atmospheric pressure, the volume of helium gas will be

The volume of given mass of a gas is decreased by $7\%$ at constant temperature. The pressure should be increased by

How much should the pressure be increased in order to reduce the volume of a given mass of gas by $5\%$ at the constant temperature?

A tyre of a vehicle is filled with air having pressure 270 kPa at $27^\circ\text{C}$. The air pressure in the tyre when the temperature increases to $37^\circ\text{C}$ is

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is:

(Give: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol)

Pressure of an ideal gas, contained in a closed vessel, is increased by $0.4\%$ when heated by $1^\circ\text{C}$. Its initial temperature must be:

A container of fixed volume contains a gas at 27°C. To double the pressure of the gas, the temperature of gas should be raised to _____ °C.

When the pressure of the gas contained in a closed vessel is increased by $2.3\%$, the temperature of the gas increases by 4 K. The initial temperature of the gas is

An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressures at temperature $27^\circ\text{C}$. The mass of the oxygen withdrawn from the cylinder is nearly equal to:

[Given, $R = \frac{100}{12}\text{ J mol}^{-1}\text{ K}^{-1}$, and molecular mass of $\text{O}_2 = 32,\ 1$ atm pressure $= 1.01 \times 10^{5}\text{ N/m}^{2}$]

The pressure ' P ', volume ' V ' and temperature ' T ' of a gas in a jar ' $A$ ' and the gas in other jar ' $B$ ' is at pressure ' 2 P ', volume ' $\frac{V}{4}$ ' and temperature ' $\frac{T}{4}$ '. Then the ratio of the number of molecules in jar A and jar B will be

For an ideal gas, the density of the gas is $\rho_0$ when temperature and pressure of the gas are $T_0$ and $P_0$ respectively. when the temperature of the gas is $2T_0$, its pressure becomes $3P_0$. The new density will be

An ideal gas at pressure ' P ' and temperature ' T ' is enclosed in a vessel of volume ' $V$ '. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to ' $P'$ '. Assuming that the temperature of the gas remains constant during the leakage, the number of moles of the gas that have leaked is

A container has two chambers of volumes $V_1 = 2$ litres and $V_2 = 3$ litres separated by a partition made of a thermal insulator. The chambers contain $n_1 = 5$ and $n_2 = 4$ moles of ideal gas at pressures $p_1 = 1\text{ atm}$ and $p_2 = 2\text{ atm}$, respectively. When the partition is removed, the mixture attains an equilibrium pressure of

There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K, at steady state the pressure in the vessels will be (in kPa ).

Temperature remaining constant, the pressure of gas is decreased by $20\%$. The percentage change in volume is

A gas is contained in closed vessel. The initial temperature of the gas is $100^\circ\text{C}$. If the pressure of the gas is increased by $4\%$, the increase in the temperature of the gas is

A sample of oxygen gas and a sample of hydrogen gas both have the same mass, same volume and the same pressure. The ratio of their absolute temperature is (Molecular wt. of $\text{O}_2 \,\&\, \text{H}_2$ is 32 and 2 respectively)

The following graph represents the $T\text{-}V$ curves of an ideal gas (where $T$ is the temperature and $V$ the volume) at three pressures $P_1, P_2$ and $P_3$ compared with those of Charles's law represented as dotted lines.

Then the correct relation is:

P-T diagram of an ideal gas having three different densities $\rho_1, \rho_2, \rho_3$ (in three different cases) is shown in the figure. Which of the following is correct:

The temperature of a gas having $2.0 \times 10^{25}$ molecules per cubic meter at $1.38\text{ atm}$ (Given, $k = 1.38 \times 10^{-23}\text{ J K}^{-1}$) is:

Two vessels separately contain two ideal gases A and B at the same temperature, pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of $B$. The ratio of molecular weights of $A$ and $B$ is

Two vessels $A$ and $B$ are of the same size and are at same temperature. A contains $1\text{ g}$ of hydrogen and $B$ contains $1\text{ g}$ of oxygen. $P_A$ and $P_B$ are the pressures of the gases in $A$ and $B$ respectively, then $\frac{P_A}{P_B}$ is:

At constant temperature, increasing the pressure of a gas by $5\%$ its volume will decrease by

Which one of the following represents correctly the variation of volume (V) of an ideal gas with temperature $(T)$ under constant pressure conditions?

According to Boyle's law, the product PV remains constant. The unit of $PV$ is same as that of

A bicycle tyre is filled with air having pressure of $270\text{ kPa}$ at $27^\circ\text{C}$. The approximate pressure of the air in the tyre when the temperature increases to $36^\circ\text{C}$ is

For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.

The temperature corresponding to the point '$\text{K}$' is:

A sample of oxygen gas and a sample of hydrogen gas both have the same mass, same volume and the same pressure. The ratio of their absolute temperature is

A container of volume $200\text{ cm}^{3}$ contains 0.2 mole of hydrogen gas and 0.3 mole of argon gas. The pressure of the system at temperature $200\text{ K}$ ($R = 8.3\text{ J K}^{-1}\text{ mol}^{-1}$) will be :-

The correct relation between $\gamma = \frac{c_p}{c_v}$ and temperature T is:

The pressure $(P)$ and temperature ($T)$ relationship of an ideal gas obeys the equation $PT^{2} =$ constant. The volume expansion coefficient of the gas will be:

For an ideal gas the density of the gas is $\rho_0$ when temperature and pressure of the gas are $T_0$ and $P_0$ respectively. When the temperature of the gas is $2T_0$, its pressure will be $3P_0$. The new density will be

We have a jar filled with gas characterized by parameters $P, V, T$ and another jar B filled with gas having parameters $2P, \frac{V}{4}, 2T$, where symbols have their usual meaning. The ratio of number of molecules in jar A to those in jar B is

A jar '$P$' is filled with gas having pressure, volume and temperature $P, V, T$ respectively. Another gas jar $Q$ filled with a gas having pressure $2P$, volume $\frac{V}{4}$ and temperature $2T$. The ratio of the number of molecules in jar $P$ to those in jar $Q$ is

When a gas filled in a closed vessel is heated by raising the temperature by 1$^\circ$C, its pressure increases by 0.4%. The initial temperature of the gas is ___________ K.

The volume occupied by the molecules contained in 4.5 kg water at STP, if the intermolecular forces vanish away is

A vessel contains 16g of hydrogen and 128g of oxygen at standard temperature and pressure. The volume of the vessel in cm3 is:

A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0$^\circ$C will be: (Given gas constant R = 8.3 JK${}^{-1}$-mol${}^{-1}$)

For a perfect gas, two pressures P1 and P2 are shown in figure. The graph shows:

A mixture of hydrogen and oxygen has volume 2000 cm3, temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be:

[Take gas constant R = 8.3 JK${}^{-1}$mol${}^{-1}$]

A balloon carries a total load of 185 kg at normal pressure and temperature of 27$^\circ$C. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is $-7^\circ$C. Assuming the volume constant?

An ideal gas is expanding such that PT3 = constant. The coefficient of volume expansion of the gas is:

Which of the following graphs represent the behavior of an ideal gas? Symbols have their usual meaning.

A mixture of hydrogen and oxygen has volume 500 cm3, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be :-

A cylindrical container of volume 4.0 $\times$ 10$-$3 m3 contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K. The pressure of the mixture of gases is:

[Take gas constant as 8.3 J mol${}^{-1}$ K${}^{-1}$]

A container is divided into two chambers by a partition. The volume of first chamber is 4.5 litre and second chamber is 5.5 litre. The first chamber contain 3.0 moles of gas at pressure 2.0 atm and second chamber contain 4.0 moles of gas at pressure 3.0 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 atm. Value of x is ________.

For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation $\frac{dp}{dv} = -ap$. If p = p0 at v =0 is the given boundary condition, then the maximum temperature one mole of gas can attain is: (Here R is the gas constant)

The average thermal energy for a mono-atomic gas is: (kB is Boltzmann constant and T absolute temperature)

An ideal gas equation can be written as

$P = \frac{\rho RT}{M_0}$

where $\rho$ and $M_0$ are respectively,

A cylinder contains hydrogen gas at pressure 249 kPa and temperature 27$^\circ$C

Its density is: (R = 8.3 J mol-1 K-1)

The change in the magnitude of the volume of an ideal gas when a small additional pressure $\Delta$P is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity $\Delta$T at constant pressure. The initial temperature and pressure of the gas were 300 K and 2 atm. respectively.

If |$\Delta$T| = C|$\Delta$P| then value of C in (K/atm.) is _________.

The equation of state for 2 g of oxygen at a pressure ' $P$ ' and temperature ' $T$, when occupying a volume ' $V$ ' will be

A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is: [Given that R = 8.31 J mol–1 K–1]

An ideal gas occupies a volume of 2m3 at a pressure of 3 $\times$ 106 Pa. The energy of the gas is:

The temperature of an open room of volume 30 m3 increases from 17oC to 27oC due to the sunshine. The atmospheric pressure in the room remains 1 $\times$ 105 Pa. If Ni and Nf are the number of molecules in the room before and after heating, then Nf – Ni will be:

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?

Which of the following shows the correct relationship between the pressure ‘P’ and density $\rho$ of an ideal gas at constant temperature?

Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weight of A and B is

Modern vacuum pumps can evacuate a vessel down to a pressure of 4.0 $\times$ 10$-$15 atm. at room temperature (300 K). Taking R = 8.3 JK${}^{-1}$ mole${}^{-1}$, 1 atm = 105 Pa and NAvogadro = 6 $\times$ 1023 mole${}^{-1}$, the mean distance between molecules of gas in an evacuated vessel will be of the order of:

In the given (V $-$ T) diagram, what is the relation between pressure P1 and P2?

The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from T1K to T2K is

A thin tube sealed at both ends is 100 cm long. It lies horizontally, the middle 20 cm containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced?

(Given: cross-section of the tube can be assumed to be uniform)

At 10oC the value of the density of a fixed mass of an ideal gas divided by its pressure is x. At 110oC this ratio is

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $V_1$ and contains ideal gas at pressure $P_1$ and temperature $T_1$. The other chamber has volume $V_2$ and contains ideal gas at pressure $P_2$ and temperature $T_2$. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

The equation of state for 5 g of oxygen at a pressure P and temperature T, when occupying a volume V, will be

(where R is the gas constant)

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

The gases carbon-monoxide (CO) and nitrogen at the same temperature have kinetic energies $E_1$ and $E_2$ respectively. Then

Relation between pressure ($P$) and energy ($E$) of a gas is

For hydrogen gas $C_P - C_V = a$ and for oxygen gas $C_P - C_V = b$, so the relation between $a$ and $b$ is given by

Two containers $A$ and $B$ are partly filled with water and closed. The volume of $A$ is twice that of $B$ and it contains half the amount of water in $B$. If both are at the same temperature, the water vapour in the containers will have pressure in the ratio of