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

1.		2.
3.		4.

The root-mean-square velocity of the molecules in a sample of helium is $\frac{5}{7}th$ of that of the molecules in a sample of hydrogen.  If the temperature of the hydrogen gas is 0$°$C, that of the helium sample is about:

1. 0$°$C       

2. 5.6$°$C      

3. 273$°$C         

4. 100$°$C

The kinetic energy of one gram molecule of a gas at standard temperature and pressure is: (R = 8.31 J/mol-K)

1. 0.56 $\times {10}^4 J$             

2. $1.3\times {10}^2 J$

3. $2.7\times {10}^2 J$                 

4. $3.4\times {10}^3 J$

The equation of state for 5 g of oxygen at a pressure P and temperature T, when occupying a volume V, will be: (where R is the constant)

1. PV = 5RT

2. PV = $\left(\frac{5}{2}\right)RT$

3. PV = $\left(\frac{5}{16}\right)RT$

4. PV = $\left(\frac{5}{32}\right)RT$

From the T-P graph, what conclusion can be drawn?

1. $V_2=V_1$

2. $V_2<V_1$

3. $V_2>V_1$

4. Nothing can be predicted

The root mean square speed of the molecules of an enclosed gas is V.  What will be the root mean square speed if the pressure is doubled, the temperature remaining the same?

1. $\frac{v}{2}$     

2. v         

3. 2       

4. 4 v

If the degree of freedom of gas are f, then the ratio of two specific heats $C_P/C_V$ is given by:

[MP PET 1995; BHU 1997; MP PMT 2001, 04]

1. $\frac{2}{f}+1$                 

 2. $1-\frac{2}{f}$

3. $1+\frac{1}{f}$                   

4. $1-\frac{1}{f}$

The molecular weight of two gases is \(M_1\) and \(M_2.\) At any temperature, the ratio of root mean square velocities \(v_1\) and \(v_2\) will be:
1. \(\sqrt{\frac{M_1}{M_2}}\)
2. \(\sqrt{\frac{M_2}{M_1}}\)
3. \(\sqrt{\frac{M_1+M_2}{M_1-M_2}}\)
4. \(\sqrt{\frac{M_1-M_2}{M_1+M_2}}\)

An ideal gas is found to obey an additional law $V{P}^2$= constant. The gas is initially at temperature T and volume V. When it expands to a volume 2 V, the temperature becomes:

1. T $\sqrt{2}$         

2. 2T       

3. 2T$\sqrt{2}$           

4. 4T

The figure shows two connected flasks. The volume of flask-1 is twice that of flask-2. The system is filled with an ideal gas at temperatures of \(100\) K and \(200\) K, respectively. If the mass of the gas in flask-1 is \(m,\) what is the mass of the gas in flask-2 when the system reaches equilibrium?

      
1. \(m\)         
2. \(m/2\)    
3. \(m/4\)    
4. \(m/8\)