Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Air is Pumped into the Tubes of a Cycle Rickshaw at a Pressure of 2 Atm. the Volume of Each Tube at this Pressure is 0.002 M3. One of the Tubes Gets Punctured and the Volume - Physics

Sum

Air is pumped into the tubes of a cycle rickshaw at a pressure of 2 atm. The volume of each tube at this pressure is 0.002 m3. One of the tubes gets punctured and the volume of the tube reduces to 0.0005 m3. How many moles of air have leaked out? Assume that the temperature remains constant at 300 K and that the air behaves as an ideal gas.

Use R = 8.3 J K-1 mol-1

#### Solution

Here,
P1 = 2 × 105 pa
V1 = 0.002 m3
V2 = 0.0005 m3
T1 = T2 = 300 K
Number of moles initially , n1 = $\frac{P_1 V_1}{R T_1}$
⇒  n1 = $\frac{2 × {10}^5 \times 0.002}{8.3 × 300}$
⇒ n1 = 0.16
Applying equation of state, we get
P2 V2 = n2 RT
Assuming the final pressure becomes equal to the atmospheric pressure, we get
P2 = 1.0 × 105 pa
⇒ n2 = $\frac{P_2 V_2}{RT}$
⇒ n2 = $\frac{1.0 × {10}^5 × 0.0005}{8.3 × 300}$
⇒ n2 = 0.02
Number of leaked moles= n2 - n1
= 0.16 -0.02
= 0.14

Concept: Kinetic Theory of Gases and Radiation - Kinetic Interpretation of Temperature
Is there an error in this question or solution?

#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 2 Kinetic Theory of Gases
Q 26 | Page 35