Question: At the top of a mountain a thermometer reads 7<sup>0</sup>C and a barometer reads 70 cm of Hg. At th...

Question

At the top of a mountain a thermometer reads 7⁰C and a barometer reads 70 cm of Hg. At the bottom of the mountain these read 27⁰C and 76 cm of Hg respectively. Comparison of density of air at the top with that of bottom is

Answer 1

Solution

$V_{1} = 2.4 \times 10^{- 3}m^{3}$ , $P_{1} = P_{0} = 10^{5}\frac{N}{m^{2}}$ and

T₁ = 300 K (given)

If area of cross-section of piston is A and it moves through distance x then increment in volume of the gas = Ax

and if force constant of a spring is k then force F = kx and pressure = $\frac{F}{A} = \frac{kx}{A}$

$V_{2} = V_{1} + Ax = 2.4 \times 10^{- 3} + 8 \times 10^{- 3} \times 0.1 = 3.2 \times 10^{- 3}$ and $P_{2} = P_{0} + \frac{kx}{A} = 10^{5} + \frac{8000 \times 0.1}{8 \times 10^{- 3}} = 2 \times 10^{5}$

From ideal gas equation $\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}$ ⇒ $\frac{10^{5} \times 2.4 \times 10^{- 3}}{300} = \frac{2 \times 10^{5} \times 3.2 \times 10^{- 3}}{T_{2}}$

⇒ $T_{2} = 800K$