Q. 405.0( 1 Vote )

# Figure shows a cylindrical tube of radius 5 cm and length 20 cm. It is closed by a tight-fitting cork. The friction coefficient between the cork and the tube is 0.20. The tube contains an ideal gas at a pressure of 1 atm and a temperature of 300 K. The tube is slowly heated, and it is found that the cork pops out when the temperature reaches 600 K. Let dN denote the magnitude of the normal contact force exerted by a small length dl of the cork along the periphery (see the figure). Assuming that the temperature of the gas is uniform at any instant, calculate dN/dl. Given

Pressure of gas P1=1atm=105Pa

So, area of tube = (0.05)2

Length of tube =20cm=0.2m

So, volume=area length

Volume of cylindrical tube = (0.05)2 0.2=0.0016m2

Initial temperature T1 =300K

Final temperature T2=600K

Coefficient of friction =0.2

Let final pressure be P2. So, volume of the gas remains same until pressure becomes P2 and then corks pop out. Number of moles will also be same. So, we can apply ideal gas equation which is

PV=nRT

Where V= volume of gas

R=gas constant =8.3JK-1mol-1

T=temperature

n=number of moles of gas

P=pressure of gas.   Net pressure on cork = P2-P1=2 105 - 105=105Pa

We know that So, force acting on the cork=pressure on cork area of cork

F=105 (0.05)2

According to law of friction,

F= N

Where F=force of friction

N=normal to the surface of cork =coffieicent of friction

Now, friction is always equal to the applied force until body starts to slide.

So, In question N is denoted as dN. So, N=dN

And dl=length of cork around periphery of cork i.e. dl=circumference of cork. Thus, the value of .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Rotational Kinetic Energy43 mins  Fall in Love with INORGANIC with Gaurav Sir : Noble Gases30 mins  Colligative Properties {Theory}34 mins  Electric Flux - Theory46 mins  Wheatstone Bridge - Theory Class35 mins  Arrhenius equation & Collision Theory59 mins  VSEPR theory | Concepts at fingertips51 mins  Superfast Revision of Potential & Potenial Energy (Theory + Interactive Quiz)47 mins  DNA Fingerprinting42 mins  Meselson and Stahl experiment49 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 