There are two vessels filled with an ideal gas where volume of on… - Vidyadip

MCQ

There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K . If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K , at steady state the pressure in the vessels will be (in kPa ).

A
4.4
B
6
C
24
D
18

✓

Answer

Number of masses will remain constant
$ n _1+ n _2= n _{ f } $
$\frac{ P _1 V_1}{ RT _1}+\frac{ P _2 V_2}{ RT _2}=\frac{ P _{ f } V _{ f }}{ RT _{ f }} $
$\frac{8 \times 2 V}{ R \times 1000}+\frac{7 \times V }{ R \times 500}=\frac{ P _{ f }(3 V)}{ R \times 600} $
$\frac{16}{1000}+\frac{14}{1000}=\frac{ P _{ f }}{ R \times 600} $
$\frac{30}{1000}=\frac{ P _{ f }}{200} $
$P _{ f }=6 kPa$

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