List of top Physics Questions on Ideal gas equation asked in JEE Main

The equation of state of a real gas is given by \[ \left( P + \frac{a}{V^2} \right)(V - b) = RT, \] where \( P, V \) and \( T \) are pressure, volume and temperature respectively and \( R \) is the universal gas constant. The dimensions of \[ \frac{a}{b^2} \] is similar to that of :
Match List I with List II :
List I List II
A3 Translational degrees of freedomIMonoatomic gases
B3 Translational, 2 rotational degrees of freedomsIIPolyatomic gases
C3 Translational, 2 rotational and 1 vibrational degrees of freedomIIIRigid diatomic gases
D3 Translational, 3 rotational and more than one vibrational degrees of freedomIVNonrigid diatomic gases
Choose the correct answer from the options given below:
A flask contains Hydrogen and Argon in the ratio 2:1 by mass. The temperature of the mixture is 30°C. The ratio of average kinetic energy per molecule of the two gases (K argon/K hydrogen) is:
(Given: Atomic Weight of Ar = 39.9)

The correct relation between $\gamma=\frac{ c _{ p }}{ c _{ v }}$ and temperature $T$ is :

An air bubble having volume 1 cm3 at depth 40 m inside water comes to the surface. What will be the volume of the bubble at the surface?
The temperature of an ideal gas is increased from 200 K to 800 K. If r.m.s. speed of gas at 200K is v0. Then, r.m.s. speed of the gas at 800 K will be
A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,
Initial volume of 1 mole of a monoatomic gas is 2 litres. It is expanded isothermally to a volume of 6 litres. Change in internal energy is xR. Find x.
The temperature at which the kinetic energy of oxygen molecules becomes double than its value at 27°C is
A gas is compressed adiabatically, which one of the follwing statement is NOT true.
In the equation \(\bigg[X + {\frac{a}{Y^2}}\bigg] [Y - b] = RT\), X is pressure, Y is volume, R is universal gas constant and T is temperature. The physical quantity equivalent to the ratio \(\frac{a}{b}\) is 
An electron in a hydrogen atom revolves around its nucleus with a speed of 6.76 × 106 ms-1 in an orbit of radius 0.52 A°. The magnetic field produced at the nucleus of the hydrogen atom is _______T.

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.

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed ν and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by(R = universal gas constant
Following statements are given:
(A) The average kinetic energy of a gas molecule decreases when the temperature is reduced.
(B) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
(C) The average kinetic energy of a gas molecule decreases with increase in volume.
(D) Pressure of a gas increases with increase in temperature at constant pressure.
(E) The volume of gas decreases with increase in temperature.
Choose the correct answer from the options given below:

In van der Wall equation

\([P=\frac{a}{V^2}[v-b]=RT;\)

P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants a/b is dimensionally equal to:

A gas has n degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be
When a gas filled in a closed vessel is heated by raising the temperature by 1ºC, its pressure increases by 0.4%. The initial temperature of the gas is _____ K.
For a perfect gas, two pressures \(P_1\) and \(P_2\) are shown in the figure. The graph shows:
Which of the following graph correctly represent the variation δ=dVVdT for an ideal gas at constant pressure?