Kinetic Theory of Gases

The temperature of an open room of volume 30 m$^3$ increases from 17°C to 27°C due to the sunshine. The atmospheric pressure in the room remains $1\times10^5$ Pa. If $n_i$ and $n_f$ are the number of molecules in the room before and after heating, then $n_f-n_i$ will be :

An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is :

(Take $C_v=1.5$ R, where R is gas constant)

An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure ($C_p$) and at constant volume ($C_v$) is :

For the P-V diagram given for an ideal gas,

out of the following which one correctly represents the T-P diagram ?

N moles of a diatomic gas in a cylinder are at a temperature T. Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas ?

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by $PV^n$ = constant, then n is given by (Here $C_P$ and $C_V$ are molar specific heat at constant pressure and constant volume, respectively) :

'n' moles of an ideal gas undergoes a process A→B as shown in the figure. The maximum temperature of the gas during the process will be :

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is :

Which of the following shows the correct relationship between the pressure 'P' and density ρ of an ideal gas at constant temperature ?

A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature $T$. Assuming the gases are ideal, the correct statement(s) is(are)

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $V^q$, where V is the volume of the gas. The value of q is :
$$\left(\gamma=\frac{C_p}{C_v}\right)$$

In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as $T^q$. A good estimate for q is :

Using equipartition of energy, the specific heat (in J kg$^{-1}$ K$^{-1}$) of aluminium at room temperature can be estimated to be (atomic weight of aluminium = 27)

Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the final temperature of the gases will be

Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. Then total work done by the gases till the time they achieve equilibrium will be

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement :

An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm. What will be length of the air column above mercury in the tube now ?

(Atmospheric pressure $=76$ cm of Hg)

The equation of state for a gas is given by $PV=nRT+\alpha V$, where $n$ is the number of moles and $\alpha$ is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are $T_o$ and $P_o$ respectively. The work done by the gas when its temperature doubles isobarically will be :

Modern vacuum pumps can evacuate a vessel down to a pressure of $4.0\times10^{-15}$ atm. at room temperature (300 K). Taking $R=8.3$ JK$^{-1}$ mole$^{-1}$, 1 atm $=10^5$ Pa and $N_{\text{Avogadro}}=6\times10^{23}$ mole$^{-1}$, the mean distance between molecules of gas in an evacuated vessel will be of the order of :

An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section $8.0\times10^{-3}$ m$^2$. Initially the gas is at 300K and occupies a volume of $2.4\times10^{-3}$ m$^3$ and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is $1.0\times10^5$ N/m$^2$. The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be :

(Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible)