Question

A barometer tube 90 cm long contains some air above mercury. The reading is 74.8 cm when true atmospheric pressure is 76 cm and temperature is 30${}^o$ C. If the reading is observed to be 75.4 cm on a day when temperature is 10${}^o$C, then find the true pressure.

• A. 76.07 cm
• B. 75.6 cm
• C. 76.57 cm
• D. 77.123 cm

Answer 1

The correct option is C 76.57 cm

Let A be the area of the cross-section
$V_1=(90-74.8)A=15.2Ac{m}^3$
$P_1=76-74.8=1.2$ cm of Hg
$P_2=(P-75.4)$ cm of Hg
$V_2=(90-75.4)A=14.6Ac{m}^3$
$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}=\frac{1.2\times 15.2\times 283}{303\times 14.6}=75.4+1.17$
$=76.57$ cm of Hg