Heat transferred to pressure cooker with water and energy loss

[Shakoa]

Homework Statement

I'm stuck on this thermal dynamics problem. It states: "A 2.0 kg quantity of water is held at constant volume in a puressure cooker and is heated by a range elment. The system's interal energy increases by 8.0 x 10^3 J. However, the pressure cooker is not well insulated, and 2.0 x 10^3 J of energy is transferred to the surrounding air. How much energy is trasferred from te range elment to the pressure cooker as heat?"

Homework Equations

It's an isovolumatic instance, I think, and I'm using ΔU = Q - W, where W = 0 because of the constant volume.
U is internal energy, Q is heat, W is work.

The Attempt at a Solution

I got to this:

ΔU = 8.0 x 10^3 J
W = 0
Q = 8.0 x 10^3 J
However, I don't know where to go from here. The book says that the answer is 1.00 x 10^4. I can't get there. I tried being stupid and doing this: 8.0 x 10^3 - 2.0 x 10^3, but that obviously doesn't work.

I looked at other forums with this question, but Q'=Q makes no sense.

 

[collinsmark]

Hello Shakoa,

Welcome to Physics Forums!

The book says that the answer is 1.00 x 10^3.

Are you sure the book's answer is 1.00 x 10³ J and not 1.00 x 10⁴ J (i.e. 10.0 x 10³ J)?

 

[Shakoa]

Oh, yea, it does. Sorry. Typing error. New keyboard.

I still can't get a "1" in general.

 

[collinsmark]

Okay, then.

The water/pressure cooker system increases its energy by 8.0 x 10³ J. The air increases its energy by 2.0 x 10³ J. What is the total increase in energy? Where is all this energy coming from?

 

[Shakoa]

:V The heat comes from the heating element? Do I add it? That seems like it would make sense.

 

[collinsmark]

:V The heat comes from the heating element? Do I add it? That seems like it would make sense.

Just map out where the heat (energy) comes from and where it goes.

A total of "x" amount of heat initially goes into the cooker/water sytem; however, the cooker/water system retains only 8.0 x 10³ J, while the remaining 2.0 x 10³ J is released into the air. So how much is x?

[Edit: If y apples are put into a basket, and 2 apples fall out of the basket, leaving 8 apples still in the basket at the end, how many apples y were originally put into the basket?]

 

[Shakoa]

*headdesk* >.< I feel stupid now, and I'll feel stupid if this is wrong... x = 10000/all the heat/1 x 10^4

 

[collinsmark]

*headdesk* >.< I feel stupid now, and I'll feel stupid if this is wrong... x = 10000/all the heat/1 x 10^4

That sounds right to me. The total heat is 10.0 x 10³ J. That was the amount of heat transferred to the pressure cooker (and water system), before some of it was lost to the air.

 

[Shakoa]

Very thank you muy merci. :D Thank you bunches! <3