On the basis of kinetic theory of gases, the gas exerts pressure because its molecules:

1.	continuously lose their energy till it reaches wall.
2.	are attracted by the walls of container.
3.	continuously stick to the walls of container.
4.	suffer change in momentum when impinge on the walls of container.

The root mean square speed of molecules of a given mass of a gas at \(27^\circ \text{C}\) and \(1~\text{atm}\) is \(200~\text{m/s}\) The root mean square speed of molecules of the gas at \(127^\circ \text{C}\) and \(2~\text{atm}\) will be:

Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of \(T.\) The total internal energy, \(U\) of a mole of this gas, and the value of \(\gamma~\left(=\dfrac{C_P}{C_V}\right )\) are, respectively:
1. \( U=5 R T \text { and } \gamma=\dfrac{7}{5} \)

2. \( U=\dfrac{5}{2} R T \text { and } \gamma=\dfrac{6}{5} \)

3. \(U=5 R T \text { and } \gamma=\dfrac{6}{5} \)

4. \( U=\dfrac{5}{2} R T \text { and } \gamma=\dfrac{7}{5}\)

Initially, a gas of diatomic molecules is contained in a cylinder of volume \(V_1\) at a pressure \(P_1\) and temperature \(250~\text{K}.\) Assume that \(25\%\) of the molecules get dissociated, causing a change in the number of moles. The pressure of the resulting gas at temperature \(2000~\text{K},\) when contained in a volume \(2V_1\) is given by \(P_2.\) The ratio \(P_2/P_1\) is:
1. \(2\)
2. \(3\)
3. \(5\)
4. \(9\)

The temperature of an open room of volume \(30~\text{m}^3\) increases from \(17^\circ \text{C}\) to \(27^\circ \text{C}\) due to the sunshine. The atmospheric pressure in the room remains \(1\times 10^{5}~\text{Pa}\). In \(n_i\) and \(n_f\) are the number of molecules in the room before and after heating, the \(n_f\text-n_i \) will be:
1. \( -1.61 \times 10^{23} \)
2. \( 1.38 \times 10^{23} \)
3. \( 2.5 \times 10^{25} \)
4. \( -2.5 \times 10^{25}\)

The internal energy (\(U\)), pressure (\(P\)), and volume (\(V\)) of an ideal gas are related as \(U=3PV+4\). The gas is:

If the ratio of the number density per cm³ of the two gases is \(5:3\) and the ratio of the diameters of the molecules of the two gases is \(4:5,\) then, the ratio of the mean free path of molecules of two gases is:

The mass of a hydrogen molecule is \(3.32 \times 10^{-27}~\text{kg}.\) If \(10^{23}\) hydrogen molecules strike, per second, a fixed wall of area \(2~\text{cm}^2\) at an angle of \(45^\circ\) to the normal, and rebound elastically with a speed of \(10^3~\text{m/s},\) then the pressure on the wall is nearly:
1. \( 2.35 \times 10^3 ~\text{N/m}^2 \)
2. \(4.70 \times 10^3 ~\text{N/m}^2 \)
3. \(2.35 \times 10^2 ~\text{N/m}^2 \)
4. \(4.70 \times 10^2 ~\text{N/m}^2 \)

Two moles of an ideal monoatomic gas occupy a volume \(V\) at \(27^\circ \text{C}\). The gas expands adiabatically to a volume \(2V\). Calculate the final temperature of the gas and the change in its internal energy:
1. \(189~\text{K}, ~2.7~\text{kJ}~\)
2. \(195~\text{K}, ~-2.7~\text{kJ}~\)
3. \(189~\text{K}, ~-2.7~\text{kJ}~\)
4. \(195~\text{K}, ~2.7~\text{kJ}~\)

Given below are two statements :

In the light of the above statements, choose the correct answer from the options given below :