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Question

For a fixed amount of ideal gas, match the two Lists.

A
A - Q; B - P; C - R; D - S
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B
A - S; B - R; C - S; D - R
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C
A - Q; B - P; C - S; D - R
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D
A - Q; B - S; C - R; D - Q
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Solution

The correct option is A A - Q; B - P; C - R; D - S
(A) We know that, PV=nRT ...........(1)
So, at constant P, V is directly proportional to T (Charles' law)
Taking log we get,
logV=lognRP+logT
Comparing the above equation with the equation of a straight line,Y=C+mx
As Intercept (nRP),P
So, the one with less inercept will have higher P
Hence, P1>P2>P3

(B) Dividing equation (1) by V2 we get,
PV=nRT×1V2
Comparing the above equation with the equation of a straight line,Y=C+mx
Slope is nRT and C=0
So, higher the T, higher the slope.
We can see that curve T3 has the highest slope. So, T3 is the highest.
So, T1<T2<T3

(C) Density (d) is given as:
d=PMRT
Comparing the above equation with the equation of a straight line,Y=C+mx
Slope is MRT
So, higher the T, lower the slope.
So, T1 is the highest as its slope is the lowest.
T1>T2>T3

(D) From equation (1) we can write,
V=nR×TP
Comparing the above equation with the equation of straight line,Y=C+mx
Slope =nRP
Higher the slope, smaller the P.
P3>P2>P1

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