The coefficient of performance of a refrigerator is 5.0.

a. if the compressor uses 10 j of energy, how much heat is exhausted to the hot reservoir?
b. if the hot reservoir temperature is 27 degrees celsius, what is the lowest possible temperature in degrees celsius of the cold reservoir?

is the lowest possible temperature of the cold reservoir.

Explanation:

Given:

Coefficient of performance of refrigerator,

A)

We know that for a refrigerator:

Given that 10 J of energy is consumed by the compressor:

Now the by the conservation of energy the heat exhausted :

B)

Also

where:

are the absolute temperatures of high and low temperature reservoirs respectively.

is the lowest possible temperature of the cold reservoir.

Explanation:

According to the conservation of linear momentum principle, the initial momentum (before the collision) must be equal to the final momentum (after the collision):

(1)

In addition, the initial momentum is:

(2)

Where:

is the mass of the comet

is the mass of the asteroid

is the velocity of the comet, which is positive

is the velocity of the asteroid, since it is at rest

And the final momentum is:

(3)

Where:

is the final velocity

Then :

(4)

Isolating :

(5)

Finally:

This is the final velocity, which is also in the positive direction.