newt. law cooling 2 diff. equations!!!!

I apologise.. this question may be a little convoluted :rolleyes:

this problem is based on the temperature of a room....

the variable (t) is the time in hours after 4pm eg. at 5pm t=1 .... for the purpose of the question we are considering from 4pm until midnight t=0... till t=8

there are to differential equations to consider

1. dT/dt= -k(T-8) without heater And

2. dT/dt= -k(T-8)+H .... where H=2 with heater

where k is a constant relating to insulation k is approx= 0.1732867951

when t=0, T=16 and..... in d.e number 2. the H, which =2, is relating to the power of the heating system

the temperature in the room throughout the 8 hour period Cannot fall below T=15 if it does the heater automatically comes on until the temperature rises to T=16... then the heater goes off... if it goes below T=15 then the heater comes on again until T=16 and this cycle continues throughout the 8 hour period...

When the heater is ON, you use differ. equation 2

When the heater is OFF, you use D.E 1

I'm really sorry i hope this is clear!!!!!!

a. graph the fluctuation in Temperature against time for the 8 hour period and find the FIRST time, to the nearest minute, that the heater First turns OFF

b. As a percentage, find the proportion of time that the heater is ON during the 8 hour period

(i have a suspicion that the graph may have a zig zag shape ..??!!)

I am sorry if it is confusing... i have no idea how work this out because you have to use both differential equations.... someone PLEASE help me!!!!!

:confused::confused::confused::confused::confused: :confused::confused::confused::confused::confused: :confused: Thank you for your time... if you want to contact me to clarify what i have asked please fell free to email me Thanks again,

Zena

Re: 2 differential equations

Thank you for your assistance but i am still confused. i don't know what to do