**21.** Which has maximum value of mean free path ?

**22.** 4.0 gm ideal gas is filled in a bulb having volume 10 \(dm^{3}\) at a constant temperature T & constant pressure P. If 0.8 gm gas is removed from the bulb to maintain the original pressure at (T + 125)K temperature, what would be the value of T for a gas having molar mass 40 \(gm\ mole^{-1}\).

**A.** 500K

**B.** \(500^{\circ}C\)

**C.** 773K

**D.** \(773^{\circ}C\)

**Answer :** Option A

**Explanation :**

Pressure and Temperature are constant

So \(n_{1}T_{1}=n_{2}T_{2}\)

\(\frac{W_{1}}{M_{1}}\times T_{1}=\frac{W_{2}}{M_{2}}\times T_{2},\ M_{1}=M_{2}\)

\(W_{1}T_{1}=3.2(T+125)\)

\(4T=3.2T+400\)

\(\therefore 0.8T=400\)

\(\therefore T=500K\)

**23.** What would be value of ratio for RMS and average speed of gaseous molecules at a constant temperature ?

**24.**

If temperature \(T_{2} > T_{1}\), which graph of maxwell Botlzmamn distriburibution of molecular speed iscorrect ?

**25.** The RMS velocity of an ideal gas at constant pressure varies with density relates as

**26.** The ratio of rms (root mean square ) velocities for two different gases is

**A.** \(\frac{\overline{V_{1}}}{\overline{V_{2}}}=\sqrt{\frac{M_{2}}{M_{1}}}\)

**B.** \(\frac{m_{1}}{\sqrt{M_{2}}}=\frac{m_{2}}{\sqrt{M_{1}}}\)

**C.** \(\frac{\alpha _{1}}{\sqrt{M_{2}}}=\frac{\alpha _{2}}{\sqrt{M_{1}}}\)

**D.** \(\frac{\sqrt{M_{2}}}{m_{1}}=\frac{\sqrt{M_{1}}}{m_{2}}\)

**Answer :** Option B

**27.** At constant temperature, a gas is filled at 1 atm pressure in a closed container. To compress this gas to \(\left (\frac{1}{4} \right )^{th}\) of its initial volume, the pressure to be applied is

**A.** \(\frac{4}{3}\ atm\)

**B.** \(2\ atm\)

**C.** \(\frac{1}{4}\ atm\)

**D.** \(\frac{1}{3}\ atm\)

**Answer :** Option D

**28.** What is the pressure of 380 mm Hg column of a gas in pascal ?

**A.** \(5.05\times 10^{4}\ Pa\)

**B.** \(5.06\times 10^{5}\ Pa\)

**C.** \(0.505\times 10^{3}\ Pa\)

**D.** \(1.013\times 10^{5}\ Pa\)

**Answer :** Option A

**Explanation :**

\(380\ mm=380\ torr=\frac{380}{760}\ atm\)

\(\therefore 0.987\ atm=10^{5}\ Pa\)

\(\therefore \frac{380}{760}\ atm=?\)

\(\therefore 380\ mm=5.05\times 10^{4}\ Pa\)

**29.**

The graphs plotted \(V\rightarrow T\) for one mole of an ideal gas as follows , which graph represent its ideal behaviour at atmospheric pressure ?

**A.** a

**B.** b

**C.** c

**D.** d

**Answer :** Option B

**Explanation :**

At const pressure according to charles law

\(\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}=K\)

\(\therefore \frac{22.4}{273}=0.082\) .......... (I)

and \(\therefore \frac{30.6}{373}=0.082\) ..........(II)

(I) and (II) constant behaves the gas as an ideal

**30.** Helium gas is compressed to half of the volume at 303 K. It should be heated to which temperature for its volume to increase to double of its original volume ?

**A.** 303K

**B.** 606K

**C.** 1212K

**D.** \(30^{\circ}C\)

**Answer :** Option C

**Explanation :**

According to Charles’ law

\(\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}=K\) \(V_{1}=\frac{V_{1}}{2}\) at \(T_{1}=303K\)

\(\therefore T_{2}=\frac{V_{2}T_{1}}{V_{1}}\) \(V_{2}=2V_{1}\) at \(T_{2}=?\)

\(=\frac{2V_{1}\times 303}{\frac{V_{1}}{2}}\)

= 303 x 4

= 1212K