States of Matter — JEE Advanced PYQs

The cylinders, both fitted with frictionless pistons, are filled with mixtures of He and Ar gases. In the first cylinder, the masses of He and Ar are $m_1$ and $m_2$, respectively. In the second cylinder, the masses of He and Ar are $m_2$ and $m_1$, respectively t …

Molar volume $\left(V_m\right)$ of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with $V_m$ as the variable. The ratio (in $\mathrm{mol}{\mathrm{dm}}^{-3}$) of the coefficient of $V_m^2$ to the coefficient of $V_m$ for …

A closed vessel contains 10 g of an ideal gas X at 300 K, which exerts 2 atm pressure. At the same temperature, 80 g of another ideal gas Y is added to it and the pressure becomes 6 atm. The ratio of root mean square velocities of X and Y at 300 K is

A gas has a compressibility factor of 0.5 and a molar volume of $0.4{\mathrm{dm}}^3{\mathrm{mol}}^{-1}$ at a temperature of 800 K and pressure $\mathbf{x}$ atm. If it shows ideal gas behaviour at the same temperature and pressure, the molar volume will be …

If the distribution of molecular speeds of a gas is as per the figure shown below, then the ratio of the most probable, the average and the roots mean square speeds, respectively, is

In thermodynamics the P-V work done is given by

For a system undergoing a particular process, the work done is, …

Which of the following statement(s) is (are) correct regarding the root mean square speed $\left({\mathrm{U}}_{\text{rms }}\right)$ and average translational kinetic energy ( ${\epsilon }_{\text{av }}$ ) of a molecule in a gas at equilibrium ?

The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases $x$ times. The value o …

The qualitative sketches I, II and III given below show the variation of surface tension with molar concentration of three different aqueous solutions of $\mathrm{KCl}$, ${\mathrm{CH}}_3\mathrm{OH}$ and …

One mole of a monoatomic real gas satisfies the equation p(V-b) = RT where b is a constant. The relationship of interatomic potential V(r) and interatomic distance r for the gas is given by

X and Y are two volatile liquids with molar weights of $10\mathrm{g}{\mathrm{mol}}^{-1}$ and $40\mathrm{g}{\mathrm{mol}}^{-1}$ respectively. Two cotton plugs, one soaked in $\mathbf{X}$ and the other soaked in $\mathbf{Y}$, are simultaneously placed at the ends of a t …

X and Y are two volatile liquids with molar weights of $10\mathrm{g}{\mathrm{mol}}^{-1}$ and $40\mathrm{g}{\mathrm{mol}}^{-1}$ respectively. Two cotton plugs, one soaked in $\mathbf{X}$ and the other soaked in $\mathbf{Y}$, are simultaneously placed at the ends of a t …

A fixed mass 'm' of a gas is subjected to transformation of states from K to L to M to N and back to K as shown in the figure

The succeeding operations that enable this transformation of states are

A fixed mass 'm' of a gas is subjected to transformation of states from K to L to M to N and back to K as shown in the figure

The pair of isochoric processes among the transformation of states is

For one mole of a van der Waals gas when $b=0$ and $T=300\mathrm{K}$, the $PV$ vs. $1/V$ plot is shown below. The value of the van der Waals constant $a$ (atm.liter${}^2{\mathrm{mol}}^{-2}$) is

According to kinetic theory of gases

To an evacuated vessel with movable piston under external pressure of 1 atm., 0.1 mol of He and 1.0 mol of an unknown compound (vapour pressure 0.68 atm . at $0^{\circ }\mathrm{C}$ ) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases a …

The term that corrects for the attractive forces present in a real gas in the van der Waals equation is

At 400 K, the root mean square (rms) speed of a gas $\mathbf{X}$ (molecular weight $=40$ ) is equal to the most probable speed of gas $\mathbf{Y}$ at 60 K . The molecular weight of the gas $\mathbf{Y}$ is

A gas described by van der Waals equation
(A) behaves similar to an ideal gas in the limit of large molar volumes
(B) behaves similar to an ideal gas in the limit of large pressures
(C) is characterised by van der Waals coefficients that are dependent on the identity of the gas b …

Match gases under specified conditions listed in Column I with their properties/laws in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.
| (A) hydrogen gas (P=200 atm, T=273 K) | (p) …

The given graph represents the variation of Z (compressibility factor = $\frac{\text{PV}}{\text{nRT}}$) versus P, for three real gases A, B and C. Identify the only incorrect statement.