KVPY 2019 SB SX Exam Previous Papers

Question : 94 of 120

Marks: +1, -0

Two containers C

_1

and C

_2

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 C

_1

and C

_2

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 :

The gas will flow from the hot container to the cold one and the process is reversible.
The gas will flow from one container to the other till the number of moles in two containers are equal
A long time after the valve is opened, the pressure in both the containers will be 3P
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.

Validate

Solution:

PV = n_1R\ 300

and

(4V) (5P) = _400

.....(1)
⇒ gas will move from high pressure to law pressure means

C_2 \to C_1

after long time final pressure

P_0

P_0V = n'_ 1 R\ 300

and

P_0(4V) = n' _2R(400)

.....(2)

\now n_1 + n_2 =n'_1 +n'_2

⇒

{PV}/{R\ 300}+ {5PV}/{R\ 100}= {P_0V}/{R\ 300}+ {4P_0V}/{R\ 400}

=P/3+5P=P_0/3+P_0

⇒

P_0={16P}/4=4P

Now

n'_2 /n'_1={{4P_0V}/{R\ 400}}/{{P_0V}/{R\ 300}}=3

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