A heat pump releases 103.0 kcal as it removes 54.0 kcal at the evaporator coils. How much work does this heat pump ideally accomplish? The answer should be in KJ

I see this problem this way. Perhaps another tutor will look at it too.

dE = q+w
-103 = q + w
If the evaporator coils lose 54 kcal that is -54 from the coils(exothermic at the coils) which makes it + 54 kcal to the heat pump.
Then -103 = 54 + w
w = ?

Well, aren't heat pumps just the perfect multitaskers? They remove heat and do work? Talk about overachievers!

To calculate the work done by the heat pump, we need to use the first law of thermodynamics, which states that the change in internal energy is equal to the heat added minus the work done.

Now, since the heat pump is removing heat, the heat added will be negative. Let's call the work done W (because we like to keep things simple), the heat added Q, and the change in internal energy ΔU.

According to the first law of thermodynamics:
ΔU = Q - W

We know that Q is -54.0 kcal, but we need to convert it to KJ because we want to keep things metric. 1 kcal is equal to 4.184 KJ, so -54.0 kcal is -54.0 * 4.184 KJ.

Now, here comes the magic: ΔU = Q - W. In this case, ΔU is equal to 103.0 kcal (the heat released). We need to convert this to KJ as well.

Plugging in the values we have:

103.0 kcal (converted to KJ) = -54.0 kcal (converted to KJ) - W

Solving for W, we get:

W = (-54.0 kcal + 103.0 kcal) KJ

And lo and behold, after some math-ing, the work done by the heat pump is approximately 48.24 KJ.

So, this heat pump is not just a champion at removing heat, it's also a workhorse!

To find the work done by the heat pump, we can use the equation:

Work = Heat absorbed - Heat released

Given that the heat absorbed is 54.0 kcal and the heat released is 103.0 kcal, we can plug these values into the equation:

Work = 54.0 kcal - 103.0 kcal

Now, let's convert the units from kcal to kJ:

1 kcal = 4.184 kJ

Work = (54.0 kcal - 103.0 kcal) * 4.184 kJ/kcal

Work = -49.0 kcal * 4.184 kJ/kcal

Work = -204.916 kJ

The work done by the heat pump is -204.916 kJ. Note that the negative sign indicates that work is being done on the heat pump rather than by the heat pump.

To determine the amount of work done by the heat pump, we can use the First Law of Thermodynamics, which states that energy is conserved in a thermodynamic process.

The First Law of Thermodynamics can be represented as:

∆U = Q - W

Where:
∆U is the change in internal energy of the system
Q is the heat transferred to or from the system
W is the work done by or on the system

In this case, we know that Q is equal to the heat released by the heat pump, which is 103.0 kcal, and W is the work done by the heat pump, which is what we're trying to find.

However, we need to convert the given units from kcal to kJ because the answer needs to be in kJ.

1 kcal = 4.184 kJ

Therefore, 103.0 kcal = 103.0 * 4.184 kJ = 430.152 kJ

Substituting the values into the equation:

∆U = Q - W
0 = 430.152 kJ - W

Rearranging the equation, we can isolate W:

W = 430.152 kJ

Therefore, the work done by the heat pump is 430.152 kJ.