As illustrated in the figure, a cylindrical tube of radius 5 cm and length 20 cm is sealed with a tight-fitting cork. The coefficient of friction between the cork and the tube is 0.20 . Inside the tube, an ideal gas is initially at a pressure of 1 atm and a temperature of 300 K . The tube is subjected to slow heating, and the cork pops out the moment the temperature rises to 600 K . Assuming the gas temperature remai

Step-by-step solution

Let the initial pressure be P₁ = 10^5 N/m ^2 and initial temperature be T₁ = 300 K . Since the volume remains constant until the cork pops, P₁ T₁ = P₂ T₂ . P₂ = 10^5 600 300 = 2 10^5 N/m ^2 . The net outward force exerted by the gas on the cork is balanced by the maximum static friction f . f = (P₂ - P_ atm ) r^2 f = (2 10^5 - 10^5) (0.05)^2 = 10^5 0.0025 = 250 N . The total friction force is f = N_ total , where N_ total is the total normal force. N_ total = f = 250 0.20 = 1250 N . The normal force is uniformly di