Question

A uniform tube closed at both ends with a light piston in the middle contains a
gas at 27°C. If one part is heated to 127 C, the piston moves by 10 cm
Then the length of the tube containing gas at higher temperature is​

Answer 1

Explanation:

Given A uniform tube closed at both ends with a light piston in the middle contains a gas at 27°C. If one part is heated to 127 C, the piston moves by 10 cm  Then the length of the tube containing gas at higher temperature is

• So there is a light piston in the middle of a uniform tube. Initially the gas is at 27 degree C. So one of the sides is heated to 127 degree C and hence the piston moves towards the colder side.
• We need to find the length of the tube having the gas at 127 degree C.
• Now the piston is insulated and adiabatic and the piston is movable. So the piston will be in equilibrium. So the length will be l/2. Now when the gas is heated the piston moves up by 10 cm. So both the pressure is equal.
• Now the equation for ideal gas is pv = nRT
•                                      So v is proportional to T
•                                    Or V/T = constant
• Initial temperature To = 27 degree C = 27 + 273 = 300 K
• Final temperature T1 = 127 degree C = 127 + 273 = 400 K
• Now for portion of temperature increased will be
•                                       Po Vo/ To = P1V1/T1
•                            So A (l/2  ) / 300 = A (l/2 + 10) / 400
•                                   Or l/2 / 300 = l/2 + 10 / 400
•                                Or l/6 = l + 20 / 8
•                                 4l = 3l + 60
•                                   Or l = 60 cm  

Reference link will be

https://brainly.in/question/14063892