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A barometer tube 90 cm long contains some air above mercury. The reading is 74.5 cm when the true pressure is 76 cm and the temperature is 15^(0)C. If the reading is observed to be 75.8 cm on a day when the temperature is 5^(0)C, what is the true pressure ? |
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Answer» <P> Solution :Initial volume of the air,`V_(1)` = (LENGTH of the barometer TUBE - reading ) A = (90 - 74.5) A `cm^(3) = (15.5) A cm^(3)` Initial pressure of the air, `P_(1)` = True pressure - reading = 76.0 - 74.5 = 1.5 cm Initial temperature, `T_(1) = 273 + 15 = 288 K`. Final volume , `V_(2) = (90.0 - 75.8)A = 14.2 A cm^(3)` Final temperature , `T_(2) = 273 + 5 = 278` K `(P_(1) V_(1))/(T_(1)) = (P_(2)V_(2))/(T_(2)) = (1.5 xx 15.5_(1))/(288) = (P_(2)xx 14.2)/(278)` `P_(2)= (1.5 xx 15.5 xx 278)/(14.2 xx 288) = 1.58`cm The pressure = Reading + pressure of the air = 75.8 + 1.58 = 77.38 cm |
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