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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?
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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.
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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?
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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.
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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
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