JEE Main · 2019 · 12 Jan 2019 · Shift 2 · States of Matter

An open vessel at

2 7^{\circ} C

is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature at which the vessel has been heated is :

(A) $50 0^{\circ} C$
(B)500 K✓ Correct
(C) $75 0^{\circ} C$
(D)750 K

Answer: (B)

Solution

In an open vessel the pressure and volume are fixed, so

n T

stays constant as gas escapes:

n_{1} T_{1} = n_{2} T_{2}

. With two-fifths of the air gone,

n_{2} = \frac{3}{5} n_{1}

, and starting at

T_{1} = 2 7^{\circ} C = 300

300 n_{1} = \frac{3}{5} n_{1} T_{2}

, giving

T_{2} = 500

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Single correct option

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