Mechanical Engineering Exam > Mechanical Engineering Questions > Q.4) A spherical ballon of 1 m diameter conta...
Start Learning for Free
Q.4) A spherical ballon of 1 m diameter contains a gas at 150 kpa. The gas inside the ballon is heated until pressure reaches 450 kpa. During the process of heating pressure of gas inside the ballon is proportional to cube of the diameter of the ballon. What is the workdone by the gas in the ballon?
Most Upvoted Answer
Q.4) A spherical ballon of 1 m diameter contains a gas at 150 kpa. The...
Problem Statement: A spherical balloon of 1 m diameter contains a gas at 150 kPa. The gas inside the balloon is heated until pressure reaches 450 kPa. During the process of heating, the pressure of gas inside the balloon is proportional to the cube of the diameter of the balloon. Calculate the work done by the gas in the balloon.
Solution:
Assumptions:
- The balloon is assumed to be rigid.
- The gas inside the balloon is assumed to be an ideal gas.
- The process is assumed to be isobaric.
Calculations:
- Let the initial diameter of the balloon be D1 = 1 m and the initial pressure of the gas be P1 = 150 kPa.
- Let the final pressure of the gas be P2 = 450 kPa.
- Let the final diameter of the balloon be D2.
- According to the given condition, the pressure of the gas inside the balloon is proportional to the cube of the diameter of the balloon. Therefore, we can write:
P1*(D1^3) = P2*(D2^3)
- Solving for D2, we get:
D2 = [P1/P2*(D1^3)]^(1/3)
D2 = [150/450*(1^3)]^(1/3)
D2 = 0.6204 m
- The work done by the gas in the balloon can be calculated using the following formula:
W = P*(V2 - V1)
- The initial volume of the balloon can be calculated as follows:
V1 = (4/3)*π*(D1/2)^3
V1 = (4/3)*π*(0.5)^3
V1 = 0.5236 m^3
- The final volume of the balloon can be calculated as follows:
V2 = (4/3)*π*(D2/2)^3
V2 = (4/3)*π*(0.3102)^3
V2 = 0.0474 m^3
- Substituting the values in the formula for work, we get:
W = P*(V2 - V1)
W = 450*(0.0474 - 0.5236)
W = - 34.110 kJ
Conclusion: The work done by the gas in the balloon is -34.110 kJ, which indicates that the work is done by the gas on the surroundings. This is because during the heating process, the gas expands, and the surroundings do work on the gas.
Solution:
Assumptions:
- The balloon is assumed to be rigid.
- The gas inside the balloon is assumed to be an ideal gas.
- The process is assumed to be isobaric.
Calculations:
- Let the initial diameter of the balloon be D1 = 1 m and the initial pressure of the gas be P1 = 150 kPa.
- Let the final pressure of the gas be P2 = 450 kPa.
- Let the final diameter of the balloon be D2.
- According to the given condition, the pressure of the gas inside the balloon is proportional to the cube of the diameter of the balloon. Therefore, we can write:
P1*(D1^3) = P2*(D2^3)
- Solving for D2, we get:
D2 = [P1/P2*(D1^3)]^(1/3)
D2 = [150/450*(1^3)]^(1/3)
D2 = 0.6204 m
- The work done by the gas in the balloon can be calculated using the following formula:
W = P*(V2 - V1)
- The initial volume of the balloon can be calculated as follows:
V1 = (4/3)*π*(D1/2)^3
V1 = (4/3)*π*(0.5)^3
V1 = 0.5236 m^3
- The final volume of the balloon can be calculated as follows:
V2 = (4/3)*π*(D2/2)^3
V2 = (4/3)*π*(0.3102)^3
V2 = 0.0474 m^3
- Substituting the values in the formula for work, we get:
W = P*(V2 - V1)
W = 450*(0.0474 - 0.5236)
W = - 34.110 kJ
Conclusion: The work done by the gas in the balloon is -34.110 kJ, which indicates that the work is done by the gas on the surroundings. This is because during the heating process, the gas expands, and the surroundings do work on the gas.
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
Q.4) A spherical ballon of 1 m diameter contains a gas at 150 kpa. The gas inside the ballon is heated until pressure reaches 450 kpa. During the process of heating pressure of gas inside the ballon is proportional to cube of the diameter of the ballon. What is the workdone by the gas in the ballon?
Question Description
Q.4) A spherical ballon of 1 m diameter contains a gas at 150 kpa. The gas inside the ballon is heated until pressure reaches 450 kpa. During the process of heating pressure of gas inside the ballon is proportional to cube of the diameter of the ballon. What is the workdone by the gas in the ballon? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Q.4) A spherical ballon of 1 m diameter contains a gas at 150 kpa. The gas inside the ballon is heated until pressure reaches 450 kpa. During the process of heating pressure of gas inside the ballon is proportional to cube of the diameter of the ballon. What is the workdone by the gas in the ballon? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.4) A spherical ballon of 1 m diameter contains a gas at 150 kpa. The gas inside the ballon is heated until pressure reaches 450 kpa. During the process of heating pressure of gas inside the ballon is proportional to cube of the diameter of the ballon. What is the workdone by the gas in the ballon?.
Q.4) A spherical ballon of 1 m diameter contains a gas at 150 kpa. The gas inside the ballon is heated until pressure reaches 450 kpa. During the process of heating pressure of gas inside the ballon is proportional to cube of the diameter of the ballon. What is the workdone by the gas in the ballon? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Q.4) A spherical ballon of 1 m diameter contains a gas at 150 kpa. The gas inside the ballon is heated until pressure reaches 450 kpa. During the process of heating pressure of gas inside the ballon is proportional to cube of the diameter of the ballon. What is the workdone by the gas in the ballon? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.4) A spherical ballon of 1 m diameter contains a gas at 150 kpa. The gas inside the ballon is heated until pressure reaches 450 kpa. During the process of heating pressure of gas inside the ballon is proportional to cube of the diameter of the ballon. What is the workdone by the gas in the ballon?.
Solutions for Q.4) A spherical ballon of 1 m diameter contains a gas at 150 kpa. The gas inside the ballon is heated until pressure reaches 450 kpa. During the process of heating pressure of gas inside the ballon is proportional to cube of the diameter of the ballon. What is the workdone by the gas in the ballon? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of Q.4) A spherical ballon of 1 m diameter contains a gas at 150 kpa. The gas inside the ballon is heated until pressure reaches 450 kpa. During the process of heating pressure of gas inside the ballon is proportional to cube of the diameter of the ballon. What is the workdone by the gas in the ballon? defined & explained in the simplest way possible. Besides giving the explanation of
Q.4) A spherical ballon of 1 m diameter contains a gas at 150 kpa. The gas inside the ballon is heated until pressure reaches 450 kpa. During the process of heating pressure of gas inside the ballon is proportional to cube of the diameter of the ballon. What is the workdone by the gas in the ballon?, a detailed solution for Q.4) A spherical ballon of 1 m diameter contains a gas at 150 kpa. The gas inside the ballon is heated until pressure reaches 450 kpa. During the process of heating pressure of gas inside the ballon is proportional to cube of the diameter of the ballon. What is the workdone by the gas in the ballon? has been provided alongside types of Q.4) A spherical ballon of 1 m diameter contains a gas at 150 kpa. The gas inside the ballon is heated until pressure reaches 450 kpa. During the process of heating pressure of gas inside the ballon is proportional to cube of the diameter of the ballon. What is the workdone by the gas in the ballon? theory, EduRev gives you an
ample number of questions to practice Q.4) A spherical ballon of 1 m diameter contains a gas at 150 kpa. The gas inside the ballon is heated until pressure reaches 450 kpa. During the process of heating pressure of gas inside the ballon is proportional to cube of the diameter of the ballon. What is the workdone by the gas in the ballon? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup