Thermodynamics problem

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1. Sep 22, 2016

Pao44445

1. The problem statement, all variables and given/known data

A silicon electric circuit is 23 mg, when electricity flows through the circuit rising the energy by 7.4 mW but this circuit wasn't design for heat ventilation. Find the rate of how much the temperature is rising per second ( ΔT/Δt ) The specific heat of silicon is 705 J/kg.K

2. Relevant equations
Q=mcΔT

3. The attempt at a solution

I know that when the electricity flows through the circuit, it will rise the temperature and we can figure the change in temperature by find both initial and final temperature but what about time? how this factor get in the calculation?

Last edited: Sep 22, 2016
2. Sep 22, 2016

Staff: Mentor

Can you express watts in terms of other SI units?

3. Sep 22, 2016

Bystander

4. Sep 22, 2016

Pao44445

Joules per second ? it is just a rate of how much energy was transfer in 1 second, I can't plug this in Q :/

5. Sep 22, 2016

Staff: Mentor

No, but you can calculate Q/Δt

6. Sep 22, 2016

Pao44445

hmm I don't know if I am correct or not

from Q=mcΔT and ΔT/Δt
(Q/mc) / Δt = Q / (mc)Δt
7.4x10-3 J / (23x10-6kg)x(705 J/kg.K)x 1 s
= 0.46 K/s

Last edited: Sep 22, 2016
7. Sep 22, 2016

Staff: Mentor

Be careful with the mass there. Since you are given the heat capacity per gram, you can use g throughout and not convert to kg.

Also, I would find it more appropriate to take Q/Δt as a whole to be 7.4 mW instead of "assuming" 1 second.

8. Sep 22, 2016

Pao44445

edited
Then Q / (mc)Δt = W/mc
(7.4x10-3 W ) / (23x10-6kg)(705 J/kg.K)
= 0.46 K/s

but how this equation solve the problem?

Last edited: Sep 22, 2016
9. Sep 22, 2016

Staff: Mentor

You've missed a division in there.

10. Sep 22, 2016

Pao44445

oops, sorry. I've edited them and got the same answer 0.45-0.46 K/s
I think this is another pure mathematic problem :( really hate this kind of problem.

11. Sep 22, 2016

Staff: Mentor

I wouldn't say that this is "pure mathematics." Actually, you need physical insight to figure out that you have information about Q/Δt. Once you figure that out, you have
$$\frac{Q}{\Delta t} = m c \frac{\Delta T}{\Delta t}$$
and you simply need to rearrange the equation to isolate ${\Delta T}/{\Delta t}$, which is what you are asked for. Such simple algebra appears everywhere in physics, so you better get used to it (and good at it)

12. Sep 22, 2016

Pao44445

Never see that equation before :/

I don't know how come Q=mcΔT so I don't actually understand how to use it

13. Sep 22, 2016