Question 1: If a barometer were built using oil (p = 0.92 g/cm³) instead of mercury (p = 13.6 g/cm³), would the column of oil be higher than, lower than, or the same as the column of mercury at 1.00 atm? If the level is different, by what factor? Explain. (5 pts) Solution: A barometer works based on the principle that the pressure exerted by the liquid column balances atmospheric pressure. The pressure is given by: P = pgh Since the atmospheric pressure remains constant (P = 1.00 atm), the height of the liquid column is inversely proportional to its density: Step 1: Given Data PHg hol=hgx Poil • Density of mercury: PHg = 13.6 g/cm³ Density of oil: Poil = 0.92 g/cm³ • Standard height of mercury at 1.00 atm: hμg Step 2: Compute Height of Oil = 760 mm = 0.760 m 13.6 hoil = 0.760 x 0.92 hoil = 0.760 × 14.78 hoil = 11.23 m Step 3: Compare Heights Since oil is less dense than mercury, the column of oil must be much taller than that of mercury. The factor by which it is taller is: Final Answer: hail 11.23 m = 14.78 hile 0.760 m • The oil column would be higher than the mercury column. • The oil column would be 14.78 times taller than the mercury column. Explanation: Since oil is less dense, a greater height is needed to exert the same pressure as mercury. This follows from the inverse relationship between height and density in barometers. Question 2: In terms of gas laws, explain why aerosol cans explode when heated. (3 pts) Answer: Aerosol cans explode when heated because of Gay-Lussac's Law, which states that pressure and temperature are directly proportional at constant volume: P₁T2 = P2T1 Since an aerosol can is a sealed container, the volume of gas inside remains constant. As temperature increases, the kinetic energy of gas molecules inside the can increases, causing them to collide more frequently and with greater force against the walls of the container. This leads to an increase in pressure. If the pressure exceeds the can's structural limit, the can bursts or explodes. In summary, as temperature increases, pressure increases due to Gay-Lussac's Law, which can lead to the explosion of the aerosol can.
Question 1: If a barometer were built using oil (p = 0.92 g/cm³) instead of mercury (p = 13.6 g/cm³), would the column of oil be higher than, lower than, or the same as the column of mercury at 1.00 atm? If the level is different, by what factor? Explain. (5 pts) Solution: A barometer works based on the principle that the pressure exerted by the liquid column balances atmospheric pressure. The pressure is given by: P = pgh Since the atmospheric pressure remains constant (P = 1.00 atm), the height of the liquid column is inversely proportional to its density: Step 1: Given Data PHg hol=hgx Poil • Density of mercury: PHg = 13.6 g/cm³ Density of oil: Poil = 0.92 g/cm³ • Standard height of mercury at 1.00 atm: hμg Step 2: Compute Height of Oil = 760 mm = 0.760 m 13.6 hoil = 0.760 x 0.92 hoil = 0.760 × 14.78 hoil = 11.23 m Step 3: Compare Heights Since oil is less dense than mercury, the column of oil must be much taller than that of mercury. The factor by which it is taller is: Final Answer: hail 11.23 m = 14.78 hile 0.760 m • The oil column would be higher than the mercury column. • The oil column would be 14.78 times taller than the mercury column. Explanation: Since oil is less dense, a greater height is needed to exert the same pressure as mercury. This follows from the inverse relationship between height and density in barometers. Question 2: In terms of gas laws, explain why aerosol cans explode when heated. (3 pts) Answer: Aerosol cans explode when heated because of Gay-Lussac's Law, which states that pressure and temperature are directly proportional at constant volume: P₁T2 = P2T1 Since an aerosol can is a sealed container, the volume of gas inside remains constant. As temperature increases, the kinetic energy of gas molecules inside the can increases, causing them to collide more frequently and with greater force against the walls of the container. This leads to an increase in pressure. If the pressure exceeds the can's structural limit, the can bursts or explodes. In summary, as temperature increases, pressure increases due to Gay-Lussac's Law, which can lead to the explosion of the aerosol can.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.6: Solving Problems Involving Quadratic Equations
Problem 1.4E
Related questions
Question
Transcribed Image Text:Question 1:
If a barometer were built using oil (p = 0.92 g/cm³) instead of mercury (p =
13.6 g/cm³), would the column of oil be higher than, lower than, or the same as the
column of mercury at 1.00 atm? If the level is different, by what factor? Explain. (5 pts)
Solution:
A barometer works based on the principle that the pressure exerted by the liquid column
balances atmospheric pressure. The pressure is given by:
P = pgh
Since the atmospheric pressure remains constant (P = 1.00 atm), the height of the
liquid column is inversely proportional to its density:
Step 1: Given Data
PHg
hol=hgx
Poil
• Density of mercury: PHg = 13.6 g/cm³
Density of oil: Poil = 0.92 g/cm³
• Standard height of mercury at 1.00 atm: hμg
Step 2: Compute Height of Oil
= 760 mm = 0.760 m
13.6
hoil
= 0.760 x
0.92
hoil
= 0.760 × 14.78
hoil
= 11.23 m
Step 3: Compare Heights
Since oil is less dense than mercury, the column of oil must be much taller than that of
mercury. The factor by which it is taller is:
Final Answer:
hail
11.23 m
= 14.78
hile
0.760 m
• The oil column would be higher than the mercury column.
• The oil column would be 14.78 times taller than the mercury column.
Explanation:
Since oil is less dense, a greater height is needed to exert the same pressure as mercury.
This follows from the inverse relationship between height and density in barometers.
Transcribed Image Text:Question 2:
In terms of gas laws, explain why aerosol cans explode when heated. (3 pts)
Answer:
Aerosol cans explode when heated because of Gay-Lussac's Law, which states that
pressure and temperature are directly proportional at constant volume:
P₁T2 = P2T1
Since an aerosol can is a sealed container, the volume of gas inside remains constant. As
temperature increases, the kinetic energy of gas molecules inside the can increases,
causing them to collide more frequently and with greater force against the walls of the
container. This leads to an increase in pressure. If the pressure exceeds the can's
structural limit, the can bursts or explodes.
In summary, as temperature increases, pressure increases due to Gay-Lussac's Law,
which can lead to the explosion of the aerosol can.
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