The molecules of a given mass of gas have RMS velocity of \(200~\text{ms}^{-1}\) at \(27^\circ \text{C}\) and \(1.0\times 10^{5}~\text{Nm}^{-2}\) pressure. When the temperature and the pressure of the gas are respectively, \(127^\circ \text{C}\) and \(0.05\times10^{5}~\text{Nm}^{-2},\) the RMS velocity of its molecules in \((\text{ms}^{-1})\) is:

1.	\(\dfrac{400}{\sqrt{3}}\)	2.	\(\dfrac{100\sqrt{2}}{3}\)
3.	\(\dfrac{100}{3}\)	4.	\(100\sqrt{2}\)

\(4.0~\text{gm}\) of gas occupies \(22.4~\text{litres}\) at NTP. The specific heat capacity of the gas at a constant volume is  \(5.0~\text{JK}^{-1}\text{mol}^{-1}.\) If the speed of sound in the gas at NTP is \(952~\text{ms}^{-1},\) then the molar heat capacity at constant pressure will be:
(\(R=8.31~\text{JK}^{-1}\text{mol}^{-1}\)) 

One mole of an ideal diatomic gas undergoes a transition from \(A\) to \(B\) along a path \(AB\) as shown in the figure. 
         
The change in internal energy of the gas during the transition is:

In the given \({(V\text{-}T)}\) diagram, what is the relation between pressure \({P_1}\) and \({P_2}\)? 

The amount of heat energy required to raise the temperature of \(1\) g of Helium at NTP, from \({T_1}\) K to \({T_2}\) K is:

Assertion The molecules of a monoatomic gas have three degrees of freedom. 

Reason The molecules of a diatomic gas have five degrees of freedom.

Assertion: The molecules of a monatomic gas has three degree of freedom. 
Reason: The molecules of a diatomic gas has five degree of freedom.

An increase in the temperature of a gas-filled container would lead to:

At what temperature will the \(\text{rms}\) speed of oxygen molecules become just sufficient for escaping from the earth's atmosphere? 
(Given: Mass of oxygen molecule \((m)= 2.76\times 10^{-26}~\text{kg}\), Boltzmann's constant \(k_B= 1.38\times10^{-23}~\text{J K}^{-1}\))
1. \(2.508\times 10^{4}~\text{K}\)
2. \(8.360\times 10^{4}~\text{K}\)
3. \(5.016\times 10^{4}~\text{K}\)
4. \(1.254\times 10^{4}~\text{K}\)