Q. At the top of the mountain the temperature is $-13^{\circ} C$ and the barometer reads $68\, cm$ of $Hg$. At the bottom the temperature is $27^{\circ} C$ and the barometer reads $70\, cm$ of $Hg$. What is the ratio of the densities of the air at the mountain to that at the sea level ?

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A

$1.03$

B

$1.12$

C

$1.15$

D

$1.24$

Solution:

We use $P=\frac{\rho R T}{M}$
$\Rightarrow \frac{P_{1}}{P_{2}}=\frac{\rho_{1}}{P_{2}} \times \frac{T_{1}}{T_{2}}$
$\Rightarrow \frac{68}{70}=\frac{\rho_{1}}{\rho_{2}}\left(\frac{260}{300}\right)$
$\Rightarrow \frac{\rho_{1}}{\rho_{2}}=1.12$

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Q. At the top of the mountain the temperature is $-13^{\circ} C$ and the barometer reads $68\, cm$ of $Hg$. At the bottom the temperature is $27^{\circ} C$ and the barometer reads $70\, cm$ of $Hg$. What is the ratio of the densities of the air at the mountain to that at the sea level ?

$1.03$

$1.12$

$1.15$

$1.24$

We use $P=\frac{\rho R T}{M}$ $\Rightarrow \frac{P_{1}}{P_{2}}=\frac{\rho_{1}}{P_{2}} \times \frac{T_{1}}{T_{2}}$ $\Rightarrow \frac{68}{70}=\frac{\rho_{1}}{\rho_{2}}\left(\frac{260}{300}\right)$ $\Rightarrow \frac{\rho_{1}}{\rho_{2}}=1.12$

Questions from Thermal Properties of Matter

1. If the temperature difference on the two sides of a wall increases from $ 100{}^\circ C $ to $ 200{}^\circ C $ , its thermal conductivity

2. A wall is made of equally thick layers $A$ and $B$ of different materials. Thermal conductivity of $A$ is twice that of $B$. In the steady state, the temperature difference across the wall is $36^{\circ}C$. The temperature difference across the layer $A$ is

3. The radiation emitted by a star $A$ is $10,000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $8000 \, K$ and $2000 \, K$ respectively. The ratio of the radii of the star $A$ and the sun is

4. A black body at $1373$ $℃$ emits maximum energy corresponding to a wavelength of $1.78$ microns. The temperature of the moon for which $\lambda _{m}=14$ micron would be

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1. If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{ E }{ G }$ has the dimensions of:

2. The de Broglie wavelength of an electron moving with kinetic energy of $144 \,eV$ is nearly

3. A car starts from rest and accelerates at $5\, m / s ^{2}$ At $t=4\, s$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t =6\, s$ ? (Take $\left. g =10\, m / s ^{2}\right)$

4. A wheel with $20$ metallic spokes each $1\, m$ long is rotated with a speed of $120\, rpm$ in a plane perpendicular to a magnetic field of $0.4\, G$. The induced emf between the axle and rim of the wheel will be, $(1 G = 10^{-4}\, T)$

5. A barometer is constructed using a liquid (density $= 760 \,kg/m^{3})$ What would be the height of the liquid column, when a mercury barometer reads $76\, cm$ ? (density of mercury $= 13600 kg/m^{3})$

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We use $P=\frac{\rho R T}{M}$
$\Rightarrow \frac{P_{1}}{P_{2}}=\frac{\rho_{1}}{P_{2}} \times \frac{T_{1}}{T_{2}}$
$\Rightarrow \frac{68}{70}=\frac{\rho_{1}}{\rho_{2}}\left(\frac{260}{300}\right)$
$\Rightarrow \frac{\rho_{1}}{\rho_{2}}=1.12$

5. A barometer is constructed using a liquid (density $= 760 \,kg/m^{3})$ What would be the height of the liquid column, when a mercury barometer reads $76\, cm$ ?
(density of mercury $= 13600 kg/m^{3})$