## Related questions with answers

An air conditioner with a power input of 1.2 kW is working as a refrigerator $(\beta=3)$ or as a heat pump $\left(\beta^{\prime}=4\right)$. It maintains an office at 20$^{\circ} \mathrm{C}$ year round that exchanges 0.5 kW per degree temperature difference with the atmosphere. Find the maximum and minimum outside temperatures for which this unit is sufficient.

Solution

VerifiedWe are given following data for air conditioner:

$\dot W=1.2\text { kW}$

$T_H=20 C$

$\dot q=0.5\frac{\text{ kW}}{\text{ C}}$

$\beta_{ref}=3$

$\beta_{pump}=4$

Heat pump COP is given by:

$\beta_{pump}=\dfrac{\dot Q_H}{\dot W}=\dfrac{\dot q\cdot (T_H-T_a)}{\dot W}$

We can solve it for ambient temperature and get minimum:

$\begin{align*} T_{min}&=T_a=T_H-\dfrac{\beta_{pump}\cdot \dot W}{\dot q}\\\\ &=20-\dfrac{4\cdot 1.2}{0.5}\\\\ &=\boxed{10.4\text{ C}} \end{align*}$

Refrigerator COP is given by:

$\beta_{ref}=-\dfrac{\dot Q_H}{\dot W}=\dfrac{\dot q\cdot (T_a-T_H)}{\dot W}$

We can solve it for ambient temperature and get maximum:

$\begin{align*} T_{max}&=T_a=T_H+\dfrac{\beta_{ref}\cdot \dot W}{\dot q}\\\\ &=20+\dfrac{3\cdot 1.2}{0.5}\\\\ &=\boxed{27.2\text{ C}} \end{align*}$

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Fundamentals of Electric Circuits

6th Edition•ISBN: 9780078028229 (2 more)Charles Alexander, Matthew Sadiku#### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th Edition•ISBN: 9780133942651 (8 more)Randall D. Knight#### Advanced Engineering Mathematics

10th Edition•ISBN: 9780470458365 (5 more)Erwin Kreyszig#### Fundamentals of Thermodynamics

8th Edition•ISBN: 9781118131992Claus Borgnakke, Richard E. Sonntag## More related questions

1/4

1/7