Solve Heat Transfer Homework: Find Constant K in kW/min

[jdawg]

Homework Statement

One kg of Refrigerant 22 initially at p1=0.9 MPa, u1=232.92 kJ/kg, is contained within a rigid closd tank. The tank is fitted with a paddle wheel that transfers energy to the refrigerant at a constant rate of 0.1kW. Heat transfer from the refrigerant to its surroundings occurs at a rate Kt, in kW, where K is a constant, in kW per minute, and t is time, in minutes. After 20 minutes of stirring, the refrigerant is at p2=1.2MPa. u2=276.7kJ/kg. Neglect kinetic and potential energy. Determine the value of the constant K appearing in the given heat transfer relation in kW/min.

Homework Equations

The Attempt at a Solution

I've already found the work to be W= -120 kJ and the heat to be Q= -76.25 kJ

What I'm struggling with is how to find the constant K.
Bounds are from 0 to 20 minutes.
Q=∫ Qdt
=∫-Kt dt
=-kt²/2

And now I'm stuck, I'm not sure what to do at this point.
The next step shows K=(-2Q)/(t²) I have no idea how they got this.

 

[insightful]

Q=∫ Qdt
=∫-Kt dt
=-kt2/2

And now I'm stuck, I'm not sure what to do at this point.
The next step shows K=(-2Q)/(t2) I have no idea how they got this.

It looks like just a rearrangement of your last equation, no?

 

[jdawg]

Haha oh my god, thanks! I forgot it was equal to Q :P