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So, I'm making a physics engine, and I need to know what is the temperature object A has after colliding with object B.

Object A is 10 earths in diameter, and is 10 earths in mass. Object B is 5 earths in diameter, and 5 in mass.

Now, A is traveling at a constant speed of 200 m/s towards B, and B is traveling at 200 m/s towards A. What would be the final temperature of A after this perfectly unelastic collision?

I know the mass, surface, initial velocity, final velocity, initial temperature and quite basically every value of both.

EDIT: I also know the kinetic energy of both.

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    $\begingroup$ What is the change in kinetic energy? $\endgroup$ – Chet Miller Nov 25 '18 at 21:42
  • $\begingroup$ I said it is a physics engine, I am not trying to calculate this value in real life. I do not know the change in kinetic energy because of that. $\endgroup$ – VetraDebesis Nov 25 '18 at 21:50
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    $\begingroup$ You said, "I also know the kinetic energy of both." Do you know how to calculate the final kinetic energy, and the change in kinetic energy? From the first law of thermodynamics, the increase in internal energy of the two masses is going to be equal to the decrease in kinetic energy from the initial state to the final state. $\endgroup$ – Chet Miller Nov 25 '18 at 21:54
  • $\begingroup$ Oh, I don't know how to calculate the change. So, the change in temperature is the smae as the change in kinetic energy? $\endgroup$ – VetraDebesis Nov 25 '18 at 22:24
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    $\begingroup$ Temperature is not a simple thing to calculate. It depends on energy input and heat capacity (which are pretty simple), but also on heat distribution, heat flow (including radiation losses) and initial temperature distribution. For planet sized masses, this is either very complex or completely unrealistic (such as by assuming no heat loss and uniform temperature distribution) $\endgroup$ – BowlOfRed Nov 25 '18 at 22:36
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Here is a way to obtain an estimate. This is for the case where the colliding masses are equal; see Chester Miller's comment below for the more general case of unequal masses.

Knowing the masses and relative velocities of the colliding objects means you know their kinetic energy content, Ek = 1/2 mv^2.

If you know what those objects are supposed to be made from (let's say iron for example), then you can look up the specific heat of iron, call it Cp. You insert this into the equation for the temperature rise that results from a certain energy input E to a given mass m of that material, E = m x Cp x (delta T).

You then assume all of the kinetic energy will be used up in heating the merged masses of the two objects. You then equate the known kinetic energy input to the temperature rise once the collision is over: 1/2mv^2 = m x Cp x (delta T) and solve for delta T.

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  • $\begingroup$ Even for an inelastic collision, conservation of momentum tells us that the final kinetic energy will not be zero. This means that only the difference between the initial and final kinetic energies will determine the temperature rise. $\endgroup$ – Chet Miller Nov 26 '18 at 13:21
  • $\begingroup$ @chestermiller, thanks for that, I made the simplifying assumption that the masses were equal but did not state it in the reply, will correct this right now. $\endgroup$ – niels nielsen Nov 26 '18 at 17:02

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