A scientist builds a "pressure thermometer" by sealing air in a tank.If the pressure inside the tank is 946 mm Hg when it is placed in a boiling water bath at 99 °C,and 749 mm Hg when left on the laboratory bench,what is the temperature in the lab?
A)295 °C
B)197 °C
C)125 °C
D)78 °C
E)22 °C

Question

Quizplus · Accepted Answer

This problem can be solved using the Gay-Lussac's Law of Pressure-Temperature, which states that the pressure of a gas is directly proportional to its temperature in kelvins. The formula is $ P_1/T_1 = P_2/T_2 $, where $ P_1 $ and $ P_2 $ are the pressures at temperatures $ T_1 $ and $ T_2 $, respectively. Given $ P_1 = 946 $ mm Hg at $ T_1 = 99 $ °C (which is 372 K, since you add 273 to convert Celsius to Kelvin) and $ P_2 = 749 $ mm Hg, we need to find $ T_2 $ in °C.Rearranging the formula to solve for $ T_2 $, we get $ T_2 = T_1 \times (P_2 / P_1) $. Plugging in the numbers: $ T_2 = 372 \times (749 / 946) $ gives $ T_2 $ in Kelvin. Converting the result back to Celsius by subtracting 273 will give the temperature in the lab, which is approximately 22 °C.

A Scientist Builds a "Pressure Thermometer" by Sealing Air in a Tank.If