In 2085, your company wins a contract to deliver oxygen to several asteroid-based habitats from another asteroid with plenty of oxygen locked up in ice. Since there is no drag in space, the size of the oxygen containers is not an issue, and the most economical method turns out to be to enclose about 6 x 105 kilograms of cold but gaseous oxygen at about half atmospheric pressure in a Mylar sphere 100 m in diameter. To the sphere, you have strapped a small rocket engine. While the engine is firing, the engine presses into the sphere roughly 10 meters, like a finger pushing in on a balloon, as the sphere accelerates. The engine exerts a constant thrust until the sphere reaches its interasteroidal cruising speed of 100 m/s. The sphere travels about 5.0 km while the engine is firing. What fraction of the energy the rocket engine has given to the sphere ends up as internal energy in the gas just before the engine shuts of
Kinetic Theory of Gas
The Kinetic Theory of gases is a classical model of gases, according to which gases are composed of molecules/particles that are in random motion. While undergoing this random motion, kinetic energy in molecules can assume random velocity across all directions. It also says that the constituent particles/molecules undergo elastic collision, which means that the total kinetic energy remains constant before and after the collision. The average kinetic energy of the particles also determines the pressure of the gas.
P-V Diagram
A P-V diagram is a very important tool of the branch of physics known as thermodynamics, which is used to analyze the working and hence the efficiency of thermodynamic engines. As the name suggests, it is used to measure the changes in pressure (P) and volume (V) corresponding to the thermodynamic system under study. The P-V diagram is used as an indicator diagram to control the given thermodynamic system.
In 2085, your company wins a contract to deliver oxygen to several asteroid-based habitats from another asteroid with plenty of oxygen locked up in ice. Since there is no drag in space, the size of the oxygen containers is not an issue, and the most economical method turns out to be to enclose about 6 x 105 kilograms of cold but gaseous oxygen at about half atmospheric pressure in a Mylar sphere 100 m in diameter. To the sphere, you have strapped a small rocket engine. While the engine is firing, the engine presses into the sphere roughly 10 meters, like a finger pushing in on a balloon, as the sphere accelerates. The engine exerts a constant thrust until the sphere reaches its interasteroidal cruising speed of 100 m/s. The sphere travels about 5.0 km while the engine is firing. What fraction of the energy the rocket engine has given to the sphere ends up as internal energy in the gas just before the engine shuts off?
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