Ideal gas equation

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]

One gas of $n_1$ mole of molecules at temperature $T_1$, volume $V_1$, and pressure $P_1$, and another gas of $n_2$ mole of molecules at temperature $T_2$, volume $V_2$, and pressure $P_2$, are mixed resulting in pressure $P$ and volume $V$ of the mixture. The temperature of the mixture is ________.

An ideal gas undergoes a process maintaining relation between pressure ($P$) and volume ($V$) as $P=P_0\left(1+\left(\dfrac{V_0}V\right)^2\right)^{-1}$, where $P_0$ and $V_0$ are constants. If two samples $A$ and $B$ (two moles each) with initial volumes $V_0$ and $3V_0$ respectively undergo above mentioned process and attain same pressure, then the difference at the temperatures of these samples, $T_B-T_A$ is ________.
($R$ = gas constant)

An ideal gas at pressure $P$ and temperature $T$ is expanding such that $PT^3$ = constant. The coefficient of volume expansion of the gas is ________.

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.

The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\dfrac32$ and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant $k$ and natural length $\dfrac{2L}{5}$. In thermodynamic equilibrium, the piston is at a distance $\dfrac{L}{2}$ from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is $P = \dfrac{kL}{A}\alpha$, then the value of $\alpha$ is _____.

A spherical soap bubble inside an air chamber at pressure $P_0 = 10^5\,\mathrm{Pa}$ has a certain radius so that the excess pressure inside the bubble is $\Delta P = 144\,\mathrm{Pa}$. Now, the chamber pressure is reduced to $8P_0/27$ so that the bubble radius and its excess pressure change. In this process, all the temperatures remain unchanged. Assume air to be an ideal gas and the excess pressure $\Delta P$ in both the cases to be much smaller than the chamber pressure. The new excess pressure $\Delta P$ in Pa is _____.

An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius 0.1 mm is dipped vertically into the liquid through the airtight piston hole, as shown in the figure. The air in the container is isothermally compressed from its original volume $V_0$ to $\dfrac{100}{101}V_0$ with the movable piston. Considering air as an ideal gas, the height $(h)$ of the liquid column in the capillary above the liquid level in cm is _____.

[Given: Surface tension of the liquid is $0.075\ \mathrm{N\,m^{-1}}$, atmospheric pressure is $10^5\ \mathrm{N\,m^{-2}}$, acceleration due to gravity $(g)$ is $10\ \mathrm{m\,s^{-2}}$, density of the liquid is $10^3\ \mathrm{kg\,m^{-3}}$ and contact angle of capillary surface with the liquid is zero]

Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is _____ $\mathrm{gm\,s^{-1}}$.

When the chimney is closed using a cap at the top, a pressure difference $\Delta P$ develops between the top and the bottom surfaces of the cap. If the changes in the temperature and density of the hot air, due to the stoppage of air flow, are negligible then the value of $\Delta P$ is _____ $\mathrm{N\,m^{-2}}$.

When a gas filled in a closed vessel is heated by raising the temperature by 1°C, its pressure increases by 0.4%. The initial temperature of the gas is ______ K.

A mixture of hydrogen and oxygen has volume 2000 cm$^3$, 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$^{-1}$]

For a perfect gas, two pressures $P_1$ and $P_2$ are shown in figure. The graph shows :

In van dar Wall equation $\left[P+\dfrac a{V^2}\right][V-b]=RT$; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants $\dfrac ab$ is dimensionally equal to :

A vessel contains 16g of hydrogen and 128 g of oxygen at standard temperature and pressure. The volume of the vessel in cm$^3$ is :

The pressure of the gas in a constant volume gas thermometer is 100 cm of mercury when placed in melting ice at 1 atm. When the bulb is placed in a liquid, the pressure becomes 180 cm of mercury. Temperature of the liquid is :

(Given 0°C = 273 K)

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is 1:4, then

A. The r.m.s. velocity of gas molecules in two vessels will be the same.

B. The ratio of pressure in these vessels will be 1:4.

C. The ratio of pressure will be 1:1.

D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of 1:4.

Choose the correct answer from the options given below :

The value of $X$ is ____.

The value of $Y$ is ____.

The value of $\dfrac{Q}{RT_0}$ is