Two 1100-kg cars are traveling 75 km/h in opposite directions ...

Question

Two 1100-kg cars are traveling 75 km/h in opposite directions when they collide and are brought to rest. Estimate the change in entropy of the universe as a result of this collision. Assume T = 20°C.

Accepted Answer

Welcome back. Everyone in this problem. Two spaceships weighing 3000 kg are speeding towards each other in outer space at 50 kilometers per hour, they collide head on and come to a complete stop because of the impact. Calculate how much change in the entropy of the universe due to this event. Assuming the surrounding temperature is 30 °C. A says it's 1813 joules per Kelvin B 1835 Joules per Kelvin C 1913 Joules per Kelvin and D 1935 joules per Kelvin. Now, if we're going to find the change in entropy of the universe, let's first make note of the information we have so far. We know that the mass of our two spaceships are 3000 kg. We also know that their speed is 50 kilometers per hour. And if we convert that to meters by a second meters per second, by multiplying by 1000 m divided by 3600 seconds, then it's 13.89 m per second. We also assume that the surrounding temperature is 30 °C. So T equals 30 °C. And if we convert that to Kelvin by adding 273.15 then our temperature is 303.15 Kelvin. So this is all the information that we have. Now, what do we know about the change in entropy? Well recall that the change in entropy of the universe. OK. Due to the collision can be approximated by the relation that considers the energy change in the form of heat transfer. In other words, it's equal to the energy dissipated or transferred as heat Q divided by the temperature T at which this energy is transferred so far, we know what T is, but we don't know what Q is. So if we can figure out the energy dissipated or transferred as heat, then we should be able to solve for the change in entropy for the universe. Now, what do we know here since we're talking about energy? Let's try to think about the energies that's involved in this collision. So we have our two spaceships. OK. Let's say that this is our spaceship and we already know what speed they're traveling together or they're speeding towards each other. OK. So let me just kind of copy and paste this here. OK. And let's just turn it on. So they're going towards each other and initially they are going towards each other with the same speed V and they have the same mass. So this is what is happening initially. So at this point, we know that both of our spaceships have kinetic energy and because their mass is the same and their speed is the same, that means their kinetic energies are also the same. Now, after, at the end of the collision, we notice our problem tells us we come, they come to a complete stop. OK. So at this point, that means that their final kinetic energy equals zero. Let me just kind of try to draw this as the collision here. These are the parts flying out and I'm probably having way too much fun with this, but this is probably what it looks like. OK. So now at this point, the kinetic energy equals zero. So that means the energy that's transferred as heat or that gets dissipated is equal to the total initial kinetic energy. What does that mean for us? We'll recall as we said, kinetic energy equals half MV squared. OK. So our total kinetic energy given that the mass and the speed are the same is going to be equal to two multiplied by half MV squared, which is going to be equal to MV squared. And no, since our heat, the energy that's transferred as heat equals the total kinetic energy, we can also find it by multiplying M by V square. So now we can go ahead and solve for the change in entropy for our universe. Because if we use this idea, that means the change in entropy is going to be equal to the total kinetic energy MV squared divided by our temperature. That's going to be equal to 3000 kg, multiplied by 13.89 m per second squared, all divided by a temperature of 303.15 Kelvin. When we go ahead and solve here and remember that this is the term that's being squared, then it should be equal to 1913.24 Joules per Kelvin. If we write that to the nearest Joule per Kelvin, it equals 1913 Jews per Kelvin. Therefore, the change in entropy of the universe as a result of the collision of the two spaceships is 1913 Jews per Kelvin. C is the correct answer. Thanks for watching everyone. I hope this video helped.

Two 1100-kg cars are traveling 75 km/h in opposite directions when they collide and are brought to rest. Estimate the change in entropy of the universe as a result of this collision. Assume T = 20°C.

Key Concepts

Conservation of Momentum

Kinetic Energy and Work-Energy Principle

Entropy and the Second Law of Thermodynamics

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