Q83 / 90 · KVPY 2019 (SB/SX) · Physics

Two containers C1 and C2 of volumes V and 4V respectively, hold the same ideal gas and are connected by a thin horizontal tube of negligible volume with a valve which is initially closed. The initial pressures of the gas in C1 and C2 are p and 5p, respectively. Heat baths are employed to maintain the temperatures in the containers at 300 K and 400 K, respectively. The valve is now opened. Select the correct statement.

  • A
    The gas will flow from the hot container to the cold one and the process is reversible.
  • B
    The gas will flow from one container to the other till the number of moles in two containers are equal.
  • C
    A long time after the valve is opened, the pressure in both the containers will be 3p.
  • Correct answer
    D
    A long time after the valve is opened, number of moles of gas in the hot container will be thrice that of the cold one.

Solution

Let n1 and n2 are number of moles of gas present in container C1 and C2 respectively, before the value is opened.

Then, using pV=nRT.

n1=pVR300

and n2=5p4VR400

Figure

When value is opened gas flows from C2 to C1 till pressure in C1 and C2 is equal. Let after equalisation of pressure in both C1 and C2, its value is p0,

Then, using pV=nRT.

p0V=n1'R300 (Container C1)

and p04V=n2'R400 (Container C2)

So, n1'=p0VR300

As no gas is leaked from containers, 

n1+n2=n1':n2'

⇒pVR300+20pVR400

=p0VR300+4p0VR400

So, p1300+20400=p01300+4400

⇒4p=p0

Now, n2'n1'=4p0VR400p0VR300=3

Finally number of moles of C2 is thrice of C1.

Hence, the correct answer is option: 'D'.

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