Question

Temperature and pressure in Delhi is ${47}^{o}C$ and 800 mm Hg whereas in Mumbai is ${27}^{o}C$ and 750 mm Hg. What is ratio of densities of air in Delhi and Mumbai?

• A. 1:1.63
• B. 1:0.957
• C. 1:1.12
• D. 1:1

Answer 1

The correct option is A 1:1.63

Given,

Temp in delhi $T_1={47}^{\circ }C$

Temp in mumbai $T_2={27}^{\circ }C$

Pressure in delhi $P_1=800mmHg$

Pressure in mumbai $P_2=750mmHg$

Now,we know

$PV=nRT$

$PV=w\times \frac{RT}{M}$

$PM=dRT$ [$d=$ density $=$ mass/volume]

$P\propto dT$ [$M$ and $R$ is constant]

$\frac{P_1}{P_2}=\frac{d_1{T}_1}{d_2{T}_2}$

$\frac{800}{750}=\frac{d_1\times 47}{d_2\times 27}$ $=1/1.63$

$d_1:d_2=1:1.63$