A faulty barometer has some trapped air above the mercury column due to which it does not give the c — States of Matter and Gaseous State Chemistry Question
Question
A faulty barometer has some trapped air above the mercury column due to which it does not give the correct reading. When the atmospheric pressure is 760 mm Hg, the barometer reads 750 mm Hg and when the pressure is 800 mm Hg, the barometer reads 770 mm Hg. The actual pressure (in mm Hg), when the barometer reads 760 mm Hg, is
💡 Solution & Explanation
Let the total length of the barometer tube above the pool be $L$. Trapped air volume $\propto (L-h)$. Pressure of trapped air $P_{air} = P_{true} - h$. Using Boyle's Law: $P_{air1}(L-h_1) = P_{air2}(L-h_2)$. For reading 1: $P_{air1} = 760 - 750 = 10\text{ mm}$, $h_1 = 750$. For reading 2: $P_{air2} = 800 - 770 = 30\text{ mm}$, $h_2 = 770$. $10(L - 750) = 30(L - 770) \implies L - 750 = 3L - 2310 \implies 2L = 1560 \implies L = 780\text{ mm}$. When $h_3 = 760\text{ mm}$, $P_{air3}(780 - 760) = 10(780 - 750) \implies P_{air3} \times 20 = 300 \implies P_{air3} = 15\text{ mm}$. True pressure $P_3 = 760 + 15 = 775\text{ mm Hg}$. Therefore, correct answer is 0775.