Kinetic Theory of Gases

List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.

Which one of the following options is correct?

0.056 kg of Nitrogen is enclosed in a vessel at a temperature of 127°C. The amount of heat required to double the speed of its molecules is ______ k cal.

(Take $R=2$ cal mole$^{-1}$K$^{-1}$)

A monoatomic gas performs a work of $\dfrac Q4$ where Q is the heat supplied to it. The molar heat capacity of the gas will be ______ R during this transformation.

Where R is the gas constant.

The relation between root mean square speed ($v_{\rm rms}$) and most probable speed ($v_p$) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :

The ratio of specific heats $\left(\dfrac{C_p}{C_v}\right)$ in terms of degree of freedom ($f$) is given by :

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 thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed $v$ 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)

A flask contains argon and oxygen in the ratio of 3:2 in mass and the mixture is kept at 27°C. The ratio of their average kinetic energy per molecule respectively will be :

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 :

According to kinetic theory of gases,

A. The motion of the gas molecules freezes at 0°C.

B. The mean free path of gas molecules decreases if the density of molecules is increased.

C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant.

D. Average kinetic energy per molecule per degree of freedom is $\frac32k_BT$ (for monoatomic gases).

Choose the most appropriate answer from the options given below:

A diatomic gas ($\gamma=1.4$) does 400J of work when it is expanded isobarically. The heat given to the gas in the process is ______ J.

The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be ______ J. (Given R = 8.31 J/mol.K)

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen ?

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°C will be :

(Given gas constant R = 8.3 JK$^{-1}$-mol$^{-1}$)

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)

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 :

Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $\sqrt2$ times the speed of sound, then the value of n will be :