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:

1.	\(\dfrac{3}{2}N_ak_B(T_2-T_1)\)	2.	\(\dfrac{3}{4}N_ak_B(T_2-T_1)\)
3.	\(\dfrac{3}{4}N_ak_B\frac{T_2}{T_1}\)	4.	\(\dfrac{3}{8}N_ak_B(T_2-T_1)\)

At \(10^{\circ}\text{C}\) the value of the density of a fixed mass of an ideal gas divided by its pressure is \(x.\) At \(110^{\circ}\text{C}\) this ratio is:

The value of $C_P-C_v=1.00$ $R$ for a gas in state A and $C_P-C_v=1.06$ $R$ in another state B. If $P_A$ $and$ $P_B$ denote the pressure and $T_A\&$ $T_B$ denote the temperatures in the two states, then:

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:

During an experiment, an ideal gas is found to obey an additional law VP² = constant. The gas is initially at temperature T and volume V. What will be the temperature of the gas when it expands to a volume 2V?

1. $\mathrm{T}\text{'}=\sqrt{4}\mathrm{T}$

2. $\mathrm{T}\text{'}=\sqrt{2}\mathrm{T}$

3. $\mathrm{T}\text{'}=\sqrt{5}\mathrm{T}$

4. $\mathrm{T}\text{'}=\sqrt{6}\mathrm{T}$

We have two vessels of equal volume, one filled with hydrogen and the other with equal mass of helium. The common temperature is \(27^{\circ}\text{C}.\) What is the relative number of molecules in the two vessels?
1. \(\frac{n_\mathrm{H}}{n_\mathrm{He}} = \frac{1}{1}\)
2. \(\frac{n_\mathrm{H}}{n_\mathrm{He}} = \frac{5}{1}\)
3. \(\frac{n_\mathrm{H}}{n_\mathrm{He}} = \frac{2}{1}\)
4. \(\frac{n_\mathrm{H}}{n_\mathrm{He}} = \frac{3}{1}\)

The volume \(V\) versus temperature \(T\) graph for a certain amount of a perfect gas at two pressures \(P_1\) and $$
\(P_2\) are shown in the figure. 

         
Here:

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. \(1.254\times 10^{4}~\text{K}\)

A gas mixture consists of \(2\) moles of \(\mathrm{O_2}\) and \(4\) moles of \(\mathrm{Ar}\) at temperature \(T.\) Neglecting all the vibrational modes, the total internal energy of the system is: