THERMODYNAMICS-SI ED. EBOOK >I<
THERMODYNAMICS-SI ED. EBOOK >I<
9th Edition
ISBN: 9781307573022
Author: CENGEL
Publisher: MCG/CREATE
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Chapter 1.11, Problem 101RP

Balloons are often filled with helium gas because it weighs only about one-seventh of what air weighs under identical conditions. The buoyancy force which can be expressed as Fb = ρairgVballoon, will push the balloon upward. If the balloon has a diameter of 12 m and carries two people 85 kg each determine the acceleration of the balloon when it is first released. Assume the density of air is ρ = 1 16 kg/m3, and neglect the weight of the ropes and the cage. Answer: 22.4 m/s2

Chapter 1.11, Problem 101RP, Balloons are often filled with helium gas because it weighs only about one-seventh of what air

Expert Solution & Answer
Check Mark
To determine

The acceleration of the balloon when it is first released.

Answer to Problem 101RP

The acceleration of the balloon when it is first released is 22.4m/s2_.

Explanation of Solution

Show the free body diagram of the balloon.

THERMODYNAMICS-SI ED. EBOOK >I<, Chapter 1.11, Problem 101RP

Write the expression of volume of sphere of a balloon.

Vballoon=4πr3/3 (I)

Write the expression of the buoyancy force acting on the balloon.

FB=ρairgVballoon (II)

Here, the density of air is ρH2O, the volume of balloon is Vballoon, and the acceleration of gravity is g.

Write the expression of the mass of helium.

mHe=ρHeVballoon (III)

Here, the density of the helium is ρHe and volume of the balloon is Vballoon.

Write the expression of the total mass can carried by balloon.

mtotal=mHe+mpeople (IV)

Here, the total mass of a people is mpeople and the mass of helium is mHe.

Write the expression of the total weight.

W=mtotalg (V)

Write the expression of net force acting on the balloon.

Fnet=FBW (VI)

Write the expression of acceleration.

a=Fnetmtotal (VII)

Conclusion:

Substitute 6m for r in Equation (I).

Vballoon=4π(6m)3/3=904.8m3.

Substitute 1.16kg/m3 for ρair, 9.81m/s2 for g, and 904.8m3 for Vballoon in Equation (II).

FB=(1.16kg/m3)(9.81m/s2)(904.8m3)=10296kgm/s2×(1N1kgm/s2)=10296N

Substitute 1.16/7kg/m3 for ρHe and 904.8m3 for Vballoon in Equation (III).

mHe=(1.167kg/m3)(904.8m3)=149.9kg.

Substitute 2×85kg for mpeople and 149.9kg for mHe in Equation (V)

mtotal=(149.9kg)+(2×85kg)=319.9kg

Substitute 319.9kg for mtotal and 9.81m/s2 for g in Equation (VI).

W=(319.9kg)(9.81m/s2)=3138kgm/s2×(1N1kgm/s2)=3138N

Substitute 10296N for FB and 3138N for W in Equation (VII).

Fnet=10296N3138N=7157N.

Substitute 7157N for Fnet and 319.9kg for mtotal in Equation (VIII).

a=(7157N)(319.9kg)=(7157N)(319.9kg)×(1kgm/s21N)=22.4m/s2

Thus, the acceleration of the balloon when it is first released is 22.4m/s2_.

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Chapter 1 Solutions

THERMODYNAMICS-SI ED. EBOOK >I<

Ch. 1.11 - The value of the gravitational acceleration g...Ch. 1.11 - A 3-kg plastic tank that has a volume of 0.2 m3 is...Ch. 1.11 - A 2-kg rock is thrown upward with a force of 200 N...Ch. 1.11 - Solve Prob. 113 using appropriate software. Print...Ch. 1.11 - A 4-kW resistance heater in a water heater runs...Ch. 1.11 - A 150-lbm astronaut took his bathroom scale (a...Ch. 1.11 - The gas tank of a car is filled with a nozzle that...Ch. 1.11 - How would you define a system to determine the...Ch. 1.11 - A large fraction of the thermal energy generated...Ch. 1.11 - A can of soft drink at room temperature is put...Ch. 1.11 - How would you define a system to determine the...Ch. 1.11 - How would you describe the state of the air in the...Ch. 1.11 - What is the difference between intensive and...Ch. 1.11 - The specific weight of a system is defined as the...Ch. 1.11 - Is the number of moles of a substance contained in...Ch. 1.11 - Is the state of the air in an isolated room...Ch. 1.11 - What is a quasi-equilibrium process? What is its...Ch. 1.11 - Define the isothermal, isobaric, and isochoric...Ch. 1.11 - What is specific gravity? How is it related to...Ch. 1.11 - What are the ordinary and absolute temperature...Ch. 1.11 - Consider an alcohol and a mercury thermometer that...Ch. 1.11 - Consider two dosed systems A and B. System A...Ch. 1.11 - Consider a system whose temperature is 18C....Ch. 1.11 - Steam enters a heat exchanger at 300 K. What is...Ch. 1.11 - The temperature of a system rises by 130C during a...Ch. 1.11 - The temperature of a system drops by 45F during a...Ch. 1.11 - The temperature of the lubricating oil in an...Ch. 1.11 - Heated air is at 150C. What is the temperature of...Ch. 1.11 - What is the difference between gage pressure and...Ch. 1.11 - Explain why some people experience nose bleeding...Ch. 1.11 - A health magazine reported that physicians...Ch. 1.11 - Someone claims that the absolute pressure in a...Ch. 1.11 - Consider two identical fans, one at sea level and...Ch. 1.11 - The absolute pressure in a compressed air tank is...Ch. 1.11 - A manometer measures a pressure difference as 40...Ch. 1.11 - A vacuum gage connected to a chambee reads 35 kPa...Ch. 1.11 - The maximum safe air pressure of a tire is...Ch. 1.11 - A pressure gage connected to a tank reads 50 psi...Ch. 1.11 - A pressure gage connected to a tank reads 500 kPa...Ch. 1.11 - A 200-pound man has a total foot imprint area of...Ch. 1.11 - The gage pressure in a liquid at a depth of 3 m is...Ch. 1.11 - The absolute pressure in water at a depth of 9 m...Ch. 1.11 - Consider a 1.75-m-tall man standing vertically in...Ch. 1.11 - The barometer of a mountain hiker reads 750 mbars...Ch. 1.11 - The basic barometer can be used to measure the...Ch. 1.11 - A gas is contained in a vertical, frictionless...Ch. 1.11 - Reconsider Prob. 158. Using appropriate software,...Ch. 1.11 - The piston of a vertical piston-cylinder device...Ch. 1.11 - Both a gage and a manometer are attached to a gas...Ch. 1.11 - Reconsider Prob. 161. Using appropriate software,...Ch. 1.11 - A manometer containing oil ( = 850 kg/m3) is...Ch. 1.11 - A manometer is used to measure the air pressure in...Ch. 1.11 - A mercury manometer ( = 13.600 kg/m3) is connected...Ch. 1.11 - Repeat Prob. 165 for a differential mercury height...Ch. 1.11 - The pressure in a natural gas pipeline is measured...Ch. 1.11 - Repeat Prob. 167E by replacing air with oil with a...Ch. 1.11 - Blood pressure is usually measure by wrapping a...Ch. 1.11 - The maximum blood pressure in the upper arm of a...Ch. 1.11 - Consider a U-tube whose arms are open to the...Ch. 1.11 - Consider a double-fluid manometer attached to an...Ch. 1.11 - Calculate the absolute pressure. P1, of the...Ch. 1.11 - Consider the manometer in Fig. 173. If the...Ch. 1.11 - Consider the manometer in Fig. 173. If the...Ch. 1.11 - The hydraulic lift in a car repair shop has an...Ch. 1.11 - Consider the system shown in Fig. 177. If a change...Ch. 1.11 - The gage pressure of the air in the tank shown in...Ch. 1.11 - Repeat Prob. 178 for a gage pressure of 40 kPa.Ch. 1.11 - What is the value of the engineering software...Ch. 1.11 - Determine a positive real root of this equation...Ch. 1.11 - Solve this system of two equations with two...Ch. 1.11 - Solve this system of three equations with three...Ch. 1.11 - Solve this system of three equations with three...Ch. 1.11 - The reactive force developed by a jet engine to...Ch. 1.11 - The reactive force developed by a jet engine to...Ch. 1.11 - A man goes to a traditional market to buy a steak...Ch. 1.11 - What is the weight of a 1-kg substance in N, kN,...Ch. 1.11 - The pressure in a steam boiler is given to be 92...Ch. 1.11 - A hydraulic lift is to be used to lift a 1900-kg...Ch. 1.11 - The average atmosphere pressure on earth is...Ch. 1.11 - Hyperthermia of 5C (i.e., 5C rise above the normal...Ch. 1.11 - The boiling temperature of water decreases by...Ch. 1.11 - A house is losing heat at a rate of 1800 kJ/h per...Ch. 1.11 - The average body temperature of a person rises by...Ch. 1.11 - The average temperature of the atmosphere in the...Ch. 1.11 - A vertical, frictionless pistoncylinder device...Ch. 1.11 - A vertical pistoncylinder device contains a gas at...Ch. 1.11 - The force generated by a spring is given by F =...Ch. 1.11 - An air-conditioning system requires a 35-m-long...Ch. 1.11 - Balloons are often filled with helium gas because...Ch. 1.11 - Reconsider Prob. 1101. Using appropriate software,...Ch. 1.11 - Determine the maximum amount of load, in kg, the...Ch. 1.11 - The lower half of a 6-m-high cylindrical container...Ch. 1.11 - A pressure cooker cooks a lot faster than an...Ch. 1.11 - The pilot of an airplane reads the altitude 6400 m...Ch. 1.11 - A glass tube is attached to a water pipe, as shown...Ch. 1.11 - Consider a U-tube whose arms are open to the...Ch. 1.11 - A water pipe is connected to a double-U manometer...Ch. 1.11 - A gasoline line is connected to a pressure gage...Ch. 1.11 - Repeat Prob. 1110 for a pressure gage reading of...Ch. 1.11 - When measuring small pressure differences with a...Ch. 1.11 - Pressure transducers are commonly used to measure...Ch. 1.11 - Consider the flow of air through a wind turbine...Ch. 1.11 - The drag force exerted on a car by air depends on...Ch. 1.11 - It is well known that cold air feels much colder...Ch. 1.11 - Reconsider Prob. 1116E. Using appropriate...Ch. 1.11 - During a heating process, the temperature of an...Ch. 1.11 - An apple loses 3.6 kJ of heat as it cools per C...Ch. 1.11 - At sea level, the weight of 1 kg mass in SI units...Ch. 1.11 - Consider a fish swimming 5 m below the free...Ch. 1.11 - The atmospheric pressures at the top and the...Ch. 1.11 - Consider a 2.5-m-deep swimming pool. The pressure...

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