Gas is found to obey the law $P^{2}V$ = constant. The initial temperature and volume are $T_0$ and $V_0$. If the gas expands to a volume $3V_0$, its final temperature becomes:

1. $\frac{T_0}{3}$           

2. $\frac{T_0}{\sqrt{3}}$

3. $3T_0$           

4. None of these

The curve between absolute temperature and \({v}^2_{rms}\)${\mathrm{}}^{}$ is:

1.		2.
3.		4.

The root-mean-square (RMS) speed of oxygen molecules $\left(O_2\right)$ at a certain absolute temperature is v. If the temperature is doubled and the oxygen gas dissociates into atomic oxygen, the RMS speed would be:

1. V                       

2. $\sqrt{2}v$

3. 2 v                     

4. 2 $\sqrt{2}v$

At what temperature is the root mean square speed of molecules of hydrogen twice as that at STP?
1. \(273~\text K\)
2. \(546~\text K\) 
3. \(819~\text K\) 
4. \(1092~\text K\) 

Volume, pressure, and temperature of an ideal gas are \(V,\) \(P,\) and \(T\) respectively. If the mass of its molecule is \(m,\) then its density is:
[\(k\)=Boltzmann's constant]

In the adjacent V-T diagram what is the relation between $P_{1 }and P_2$ ?

1. $P_2=P_1$                               

2. $P_2>P_1$

3. $P_2<P_1$                                 

4. cannot be predicated
 

Which one of the following graph is correct at constant pressure?

1.		2.
3.		4.

The equation $\left(p+\frac{a}{v^2}\right)\left(v-b\right)=RT$ is known as:

1. Perfect gas equation

2. Joule Thomson's equation

3. Vander Waal's equation

4. Maxwell's equation

The temperature of an ideal gas is increased from $27°$ to $927°C$. The r.m.s. speed of its molecules becomes-

1. twice           

2. half           

3. four times         

4. one fourth

An ideal gas is filled in a vessel, then

1. If it is placed inside a moving train, its temperature increases

2. Its centre of mass moves randomly

3. Its temperature remains constant in a moving car

4. None of these