Register to reply

Thermal physics final temperature of mixture

by AbsoluteZer0
Tags: final, mixture, physics, temperature, thermal
Share this thread:
AbsoluteZer0
#1
Feb2-13, 08:03 PM
P: 126
1. The problem statement, all variables and given/known data


250.0g of copper at 100.0C are placed in a cup containing 325.0g of water at 20.0C. Assume no heat loss to the surroundings. What is the final temperature of the copper and water?

2. Relevant equations

Conservation of Energy
mcCΔTc = mhCΔTh

3. The attempt at a solution

mcCΔTc = mhCΔTh
(0.250)(390)(Tf - Ti) = (0.325)(4200)(Tf - Ti)
(0.250)(390)(Tf - 100) = (0.325)(4200)(Tf - 20)

Have I set up my equation properly?
Phys.Org News Partner Science news on Phys.org
Bees able to spot which flowers offer best rewards before landing
Classic Lewis Carroll character inspires new ecological model
When cooperation counts: Researchers find sperm benefit from grouping together in mice
Redbelly98
#2
Feb2-13, 08:55 PM
Mentor
Redbelly98's Avatar
P: 12,068
Quote Quote by AbsoluteZer0 View Post
1. The problem statement, all variables and given/known data


250.0g of copper at 100.0C are placed in a cup containing 325.0g of water at 20.0C. Assume no heat loss to the surroundings. What is the final temperature of the copper and water?

2. Relevant equations

Conservation of Energy
mcCΔTc = mhCΔTh

3. The attempt at a solution

mcCΔTc = mhCΔTh
(0.250)(390)(Tf - Ti) = (0.325)(4200)(Tf - Ti)
(0.250)(390)(Tf - 100) = (0.325)(4200)(Tf - 20)

Have I set up my equation properly?
Almost, but not quite. Notice that you have a negative quantity on the left hand side, and a positive quantity on the right hand side -- because Tf must be somewhere between 20 and 100 C, right? So something is definitely wrong here.

Let's back up to your starting equation, which really should say

mcCcΔTc + mhChΔTh = 0

(Conservation of energy means that the total change in energy is zero.)
AbsoluteZer0
#3
Feb3-13, 01:23 PM
P: 126
mcCcΔTc + mhChΔTh = 0

(Conservation of energy means that the total change in energy is zero.)
Thanks

Hypothetically speaking, if the question asked for the the final temperature of the Copper would the set up that I used be appropriate had the final temperature of water been given?

Redbelly98
#4
Feb3-13, 09:07 PM
Mentor
Redbelly98's Avatar
P: 12,068
Thermal physics final temperature of mixture

Quote Quote by AbsoluteZer0 View Post
Thanks

Hypothetically speaking, if the question asked for the the final temperature of the Copper would the set up that I used be appropriate had the final temperature of water been given?
They would never ask it that way, since the copper and water have the same final temperature. Or did you mean to say something else?

As for your original equation, let's take a look at it again:
[tex]m_cC_c \Delta T_c = m_h C_h \Delta T_h[/tex]
Think about what it is really claiming -- it is claiming that the same amount of energy enters both the copper and the water (imagine that the ΔT's are both positive). Where is that energy supposed to come from? This claim just doesn't make sense, and the equation not saying that energy is conserved as was your intention in your original post.

We need to have a minus sign on one side of that equation. Then it would be saying the energy that leaves one substance equals the energy that enters the other substance. In other words, some energy can move from one substance to the other, and none of the energy can simply disappear, or appear out of nowhere. That is what conservation of energy means.

Note, in some examples worked out in a textbook or class lectures, people might define the ΔT's differently and write the equation you wrote. That is, for the hotter substance (copper here) they might really mean [itex]\Delta T = T_i-T_f[/itex], which is the opposite of what you called it, and equivalent to putting a minus sign in your equation as required.

Hope that helps clear things up.
AbsoluteZer0
#5
Feb3-13, 10:16 PM
P: 126
So we use

[itex] m_c C_c \Delta T_c + m_h C_h \Delta T_h = 0 [/itex]

In all questions regarding conservation of energy?
Redbelly98
#6
Feb4-13, 05:25 PM
Mentor
Redbelly98's Avatar
P: 12,068
In the ones involving heat flow between two materials, yes.

(Conservation of energy is also used in questions dealing with kinetic and potential energy. A different equation is used there.)
AbsoluteZer0
#7
Feb4-13, 07:31 PM
P: 126
Thanks


Register to reply

Related Discussions
How to determine final temperature of mixture if initial substances are at MP/FP? Introductory Physics Homework 6
Finding final temperature of a mixture Introductory Physics Homework 6
Gas mixture final temperature Introductory Physics Homework 6
Water, Ice, Steam Mixture - Final Temperature Introductory Physics Homework 1
Thermochemistry Help: Finding the final temperature of a mixture. Biology, Chemistry & Other Homework 6