Question

If P is pressure and ⍴ is density of a gas, then P and r are
related as
(a) P ∝ ⍴ (b) P ∝ (1/⍴)
(c) P ∝ ⍴² (d) P ∝ (1/⍴²)

Answer 1

If P is pressure and ⍴ is density of a gas, then P and r are

related as

(a) P ∝ ⍴

(b) P ∝ (1/⍴)

(c) P ∝ ⍴²

(d) P ∝ (1/⍴²)

Answer 2

P ∝ ⍴ is the correct relationship.

Explanation:

• According to the universal gas law, the product of the pressure and the volume of the gas is directly proportional to the product of the moles of gas and absolute temperature of the gas.

• So, PV =K.

• Or, P is proportional to V.

• Now, density is defined as mass per unit volume.

• So, ⍴ =$\frac mv$

• So, density is inversely proportional to volume.

• Combining these two relations, pressure is directly proportional to density of gas.

• Or, P ∝ ⍴.

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