Question

Gas at pressure P_o is contained in a vessel. If the masses of all the molecules are doubled and their speed is halved, the resulting pressure P will be equal to Gas at pressure P_o is contained in a vessel. If the masses of all the molecules are doubled and their speed is halved, the resulting pressure P will be equal to Gas at pressure P_o is contained in a vessel. If the masses of all the molecules are doubled and their speed is halved, the resulting pressure P will be equal t

• A. 2P_o
• B. P_o/4
• C. P_o
• D. P_o/2

Answer 1

Answer: (D)

P_o/2

Answer 2

P_o = $\frac { 1 } { 3 }$ $\left( \frac{mn}{v} \right)v_{rms}^{2}$

P = $\frac { 1 } { 3 }$ $\left( \frac{m^{'}n}{v} \right){v^{'}}_{rms}^{2}$

where m′ = 2m, $v_{rms}^{'} = \frac{v_{rms}}{2}$

putting the value

∴ $\frac{P}{P_{o}} = \frac{m^{'}{v^{'}}_{rms}^{2}}{mv_{rms}^{2}} = \frac{2m}{m}\frac{v_{rms}}{4 \times v_{rms}}$ = $\frac{1}{2}$

P = P_o/2