Question

A uniform tube closed at both ends with a piston in the middle contains a gas at27°C. If one part is heated to127°C, the piston moves by 10 cm. Then the length of the tube containing gas at higher temperature is

Answer 1

━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\large{\bf{\underline{\underline{\green{Question:-}}}}}$

A uniform tube closed at both ends with a piston in the middle contains a gas at27°C. If one part is heated to127°C, the piston moves by 10 cm. Then the length of the tube containing gas at higher temperature is

━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\large{\bf{\underline{\underline{\green{Solution:-}}}}}$

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

 

 $\implies\boxed{\bf Or l = 60 cm}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━