Teacher Xu, Please Take Care of the Reckless Students in Your Class

"As long as the observer is far enough away, despite the distance difference, the speed seen will gradually increase to approach eight-thirds."

"..."

Xu Heng thought clearly, and Qu Mingliang listened very seriously.

On the contrary, a few people around were dumbfounded.

"????"

Qu Mingliang raised his head, noticing everyone's reaction, and immediately turned over the chat records.

Only then did they understand that it was Qu Mingliang who was asking Xu Heng the question.

This was nothing, but the team leader and Teacher Fang clearly saw that Qu Mingliang sent a message to Xu Heng three minutes ago!

That is to say, three minutes ago, he sent Xu Heng three questions, and he already had the answer!

"hiss……!!!"

The first question and the second question were okay, Qu Mingliang also gave him his own ideas, and Xu Heng could still refer to it, but the third question was completely blank.

But this is what the team leader and Mr. Fang thought themselves!

Xu Heng, "You are all wrong about the second question."

Team leader, "!!!"

Teacher Fang, "!!!"

They fixed their eyes and looked at the question carefully:

A scientific expedition is stranded on a desert island after a shipwreck.

Without energy, they discovered a source of inert gas.

This gas is heavier than air, and its pressure and temperature are equal to the surrounding atmosphere.

The expedition had two membranes, one permeable to the gas and the other permeable only to air.

Try to design a working heat engine.

Xu Heng, "I won't point out where your problem is! I'll just tell my thoughts."

"There are two important laws to use here."

"If a container contains a mixture of gases, the partial pressure of each gas is equal to the pressure of that gas alone occupying the same volume at the same temperature."

"The pressure gauge reads the sum of the partial pressures in the gas mixture."

"If a membrane is permeable to a gas, the partial pressure of that gas is equal on both sides of the membrane."

"We designed such a heat engine to have a diaphragm that is permeable to inert gas in a tube that connects the gas source to the cylinder below the piston."

"Here's a sketch I'll take for you later."

"The diaphragm that is permeable to air is installed at the bottom of the cylinder. There is always the same one atmosphere of pressure below the piston, so the air does not matter to the work done."

"First, open valve [-] in the pipe to turn on the gas-permeable membrane."

"The partial pressure of the gas on both sides of the diaphragm will be equal, so there is also this partial pressure under the piston."

"As a result, the total pressure in the cylinder will reach two atmospheres, and the piston will rise to do work."

"Close valve [-] to stop the upward movement of the piston, then open valve [-] and the piston returns to its initial position without work..."

Finally, Xu Heng added, "This process is not a circular process, and we don't care about its efficiency."

"The above process can be achieved with two diaphragms, as long as there is a source of gas surrounded by a vacuum."

"Now for the last question."

Last question:

A cluster of ions of mass m spreads out at point P in different directions with the same velocity v (as shown in the figure).

A uniform magnetic field B perpendicular to the paper will focus these ions at point R, at a distance PR=2a, and the orbits of the ions should be symmetrical.

Try to determine the boundaries of the magnetic field.

"I will send you the answer, but I only wrote the general idea and the key parts. If you don't understand it, discuss it with the classmates in the class."

"Ding!"

Xu Heng took a photo and sent the idea, and said:

"In a magnetic field B, the Lorentz force acting on a particle of charge Q and velocity v is QvB. The result is that the particle moves in a circular orbit of radius r, i.e...."

"After leaving the magnetic field, they will fly straight in the direction of the last tangent."

"The boundary of the magnetic field should be searched according to the requirement that all ions hit the same point R."

"The mathematical problem to solve is where should the particles leave these circles of radius r in order for their tangents to meet at point R."

"The centers of these circles of radius r are all on the y-axis..."

"..."

"There is a quartic function here, just draw the curve of this function in the first quadrant and invert it on the y-axis."