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NEET 2008

Exam: NEET
Year: 2008
Subject: Physics
Chapter: Kinetic Theory of Gases

NEET 2008 · Physics · Kinetic Theory of Gases

At 10^ C the value of the density of a fixed mass of an ideal gas...

At

10^{\circ} \mathrm{C}

the value of the density of a fixed mass of an ideal gas divided by its pressure is

x

. At

110^{\circ} \mathrm{C}

this ratio is

Options

A $x$
B $\frac{383}{283} x$
C $\frac{10}{110} x$
D $\frac{283}{383} x$

Correct answer

D. $\frac{283}{383} x$

Step-by-step solution

Let the ratio of density and pressure be r. From Ideal Gas Equation, (\rho=\frac{\mathrm{PM}}{\mathrm{RT}})

\begin{aligned} & \mathrm{r}=\frac{\rho}{\mathrm{P}}=\frac{\mathrm{M}}{\mathrm{RT}} \\ & \therefore \frac{\mathrm{r}_2}{\mathrm{r}_1}=\frac{\mathrm{T}_1}{\mathrm{ T}_2}=\frac{273+10}{273+110}=\frac{283}{383} \\ & \mathrm{r}_2=\frac{283}{383} \quad\left(\text{ as, } \mathrm{r}_1=\mathrm{x}\right) \end{aligned}

)$

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