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# Differential Equations

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1. Can someone check my working on this question please

http://imgur.com/a/ZMXsx
2. tao =/= t
3. (Original post by iish)
tao =/= t
Why not? It's seconds, right?
4. (Original post by Naga7o)
Why not? It's seconds, right?
What? is time.
5. (Original post by Zacken)
What? is time.
V/q = volume/volumetric flow rate = time?
6. (Original post by Zacken)
What? is time.
The units of tau is seconds but that doesn't imply it's equal to t, it doesn't even imply it's a variable. In fact, the question is extremely poorly worded, I don't know if V is the initial volume or the volume as a function of time.
7. (Original post by oShahpo)
The units of tau is seconds but that doesn't imply it's equal to t.
Yeah, that's what I'm saying.
8. (Original post by Zacken)
Yeah, that's what I'm saying.
Quoted the wrong person sorry
9. (Original post by Naga7o)
V/q = volume/volumetric flow rate = time?
V is the volume as a function of time, then Volume / Volumetric flow = time if and only if the initial volume is zero. Otherwise their will be a constant.
10. (Original post by oShahpo)
V is the volume as a function of time, then Volume / Volumetric flow = time if and only if the initial volume is zero. Otherwise their will be a constant.
Would this approach be correct then?

http://imgur.com/4jbzWJz
11. (Original post by Naga7o)
Would this approach be correct then?

http://imgur.com/4jbzWJz
Between 0 and t0 C0 is a function of t, thus you haven't really separated the variables.
Your solution, I think, is correct for t>t0, for T<T0, solve this differential equation
dC/dT + C = alpha/T0 *t
This is a first differential equation that can be easily solved by finding the integrating factor.
12. (Original post by oShahpo)
Between 0 and t0 C0 is a function of t, thus you haven't really separated the variables.
Your solution, I think, is correct for t>t0, for T<T0, solve this differential equation
dC/dT + C = alpha/T0 *t
This is a first differential equation that can be easily solved by finding the integrating factor.
What happened to tau?
13. (Original post by Naga7o)
What happened to tau?
It should be there, I made a mistake. Sorry.

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