KVPY SB SX Exam 2011 Question Paper

Question : 25 of 120

Marks: +1, -0

Two bulbs of identical volumes connected by a small capillary are initially filled with an ideal gas at temperature T. Bulb 2 is heated to maintain a temperature 2T while bulb 1 remains at temperature T. Assume throughout that the heat conduction by the capillary is negligible. Then the ratio of final mass of the gas in bulb 2 to the initial mass of the gas in the same bulb is close to

$1/2$
$2/3$
$1/3$
1

Validate

Solution:

Mole conservation

n_1 + n_2 = n

Initial no. of moles

= n_1 = n_2=n/2

inally when temp of 1 vessel is T & another is 2T

n_1={\PV}/{\RT}

n_2={\PV}/{\R2\T}

⇒n_1/n_2=2/1

n_1+n_2=n

n_1={2n}/3;n_2=n/3

mass of gas

∝ n_1

∴M_2/M_1={n/3}/{n/2}=2/3

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