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

Click For Summary
SUMMARY

The discussion focuses on solving a heat transfer homework problem involving Refrigerant 22 in a rigid closed tank. The energy transfer occurs at a constant rate of 0.1 kW, and the goal is to determine the constant K in the heat transfer equation Q = -Kt. After 20 minutes, the refrigerant's state changes from p1=0.9 MPa, u1=232.92 kJ/kg to p2=1.2 MPa, u2=276.7 kJ/kg. The constant K is derived using the equation K = (-2Q)/(t^2), where Q is the total heat transfer calculated as -76.25 kJ.

PREREQUISITES
  • Understanding of thermodynamics, specifically heat transfer principles.
  • Familiarity with the properties of Refrigerant 22.
  • Knowledge of integral calculus for solving heat transfer equations.
  • Experience with energy balance calculations in closed systems.
NEXT STEPS
  • Study the derivation of the heat transfer equation Q = -Kt in thermodynamics.
  • Learn about the properties and behavior of Refrigerant 22 under varying pressures.
  • Explore integral calculus applications in thermodynamic processes.
  • Review energy balance techniques in closed systems for better understanding.
USEFUL FOR

This discussion is beneficial for students studying thermodynamics, particularly those tackling heat transfer problems in closed systems, as well as educators looking for practical examples of energy transfer calculations.

jdawg
Messages
366
Reaction score
2

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.
 
Physics news on Phys.org
jdawg said:
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?
 
  • Like
Likes   Reactions: jdawg
Haha oh my god, thanks! I forgot it was equal to Q :P
 

Similar threads

Spec'ing the power of heater for an atypical heat exchanger problem
  • · Replies 22 ·
Replies
22
Views
4K
Thermodynamics Energy transfer question
  • · Replies 10 ·
Replies
10
Views
2K
Estimate the local heat transfer flux
  • · Replies 16 ·
Replies
16
Views
4K
Steam produced heat transfer heat exchangers
  • · Replies 50 ·
2
Replies
50
Views
12K
Steam boiler efficiency calculations
  • · Replies 10 ·
Replies
10
Views
3K
Liquid ammonia is heated as it flows at a mean velocity of 2
  • · Replies 13 ·
Replies
13
Views
3K
Transient heat transfer in a sphere
  • · Replies 1 ·
Replies
1
Views
3K
Transient Energy Balance for Heating a Tank of Water
  • · Replies 4 ·
Replies
4
Views
3K
Heat transfer in polytropic process
  • · Replies 1 ·
Replies
1
Views
6K
Work done and total heat transfer for piston-cylinder device
  • · Replies 1 ·
Replies
1
Views
21K