Why does a Carnot heat pump output more heat than the work input?

[Philip Robotic]

Homework Statement

Calculate the heat Q_H that a Carnot heat pump can deliver to the reservoir with a temperature T_H. Temperature of lower reservoir (T_L) and work (W, W>0) are given

Relevant Equations

Equations come from Carnot refrigeration cycle
1. |W|=|Q_H|-|Q_L|
2. K=|Q_L|/|W|

So first I transformed the equation no 2 like this:
$$|Q_L|=K\cdot|W|$$
And then I transformed the first equation to find $|Q_Z|$
$$|Q_L|=|Q_H|-|W|$$
Plugging the result into the first equation
$$|Q_H|=K\cdot |W|+|W|$$
$$|Q_H|=|W|\cdot (K+1)$$
We know that the efficiency coefficient K is greater than 0, so how is it possible that the energy "pumped" into the hot reservoir ($Q_H$) is greater than the work that was put into the system?

 

[Chestermiller]

Homework Statement: Calculate the heat Q_H that a Carnot heat pump can deliver to the reservoir with a temperature T_H. Temperature of lower reservoir (T_L) and work (W, W>0) are given
Homework Equations: Equations come from Carnot refrigeration cycle
1. |W|=|Q_H|-|Q_L|
2. K=|Q_L|/|W|

So first I transformed the equation no 2 like this:
$$|Q_L|=K\cdot|W|$$
And then I transformed the first equation to find $|Q_Z|$
$$|Q_L|=|Q_H|-|W|$$
Plugging the result into the first equation
$$|Q_H|=K\cdot |W|+|W|$$
$$|Q_H|=|W|\cdot (K+1)$$
We know that the efficiency coefficient K is greater than 0, so how is it possible that the energy "pumped" into the hot reservoir ($Q_H$) is greater than the work that was put into the system?

The heat to the hot reservoir is the work that was put into the system plus the heat that is pumped from the cold reservoir.

 

[Philip Robotic]

So I will be able to heat up a certain substance more by using a Carnot Heat Pump than by theoretically converting all the available energy to heat? Do I understand it correctly?

 

[Chestermiller]

So I will be able to heat up a certain substance more by using a Carnot Heat Pump than by theoretically converting all the available energy to heat? Do I understand it correctly?

There is also energy available from the cold reservoir, and you’re using some of that too.

 

[Chandra Prayaga]

Did you use the information that it is a Carnot cycle?