Question

Physics help? Heat flow and thermal equilibrium?

I know this is the math section but usually there are more people online here, and I'm hoping someone can help me out.

I have do to a lab report about thermal equilibrium and heat flow. I've been given 4 experiments, and I have to find Q, or change in heat, for both objects for 3 out of the 4 experiments, if that makes sense.

First, here's some base information

In the virtual lab, there are two boxes. You connect them with a copper rod, and then wait until they reach thermal equilibrium, and then you're given the final temperatures. I'm given the thermal conductivity of the copper rod (500 watts), the length of the rod (0.75m), and the area of cross section (0.002m^2)

In experiment 1, these are the values
Both blocks are copper, each weighing 1kg. One starts at 100 degrees C, and the other at 0 degrees C. They both end at 50 degrees C.
I have to calculate the change in heat for both objects, which I know is

Q=mc(delta)T

I know the mass of the objects, but I don't know the heat capacity. Can anyone help me figure this out?

If anyone's willing to help me, I'd like some help figuring out the other two experiments values, and the fourth experiment is a little different.

Thank you in advance for your time.

Answer 1

do they ask for the time interval?

and the heat capacity of copper can be found in any textbook or online

Answer 2

I was mistaken, delta T is change in temperature, not time in this experiment.

Answer 3

indeed :)

Answer 4

Is there any way to solve this with the information I've been given by my school? It doesn't seem like I can, which is why I'm confused.

Answer 5

the heat capacity of copper is a constant that doesn't change: 0.385 J/g * C

Answer 6

J/(g*C)

Answer 7

I found it in my textbook and it says 3.87 x 10^3, 387 J/kg*C), or .387 J/g*C

So

Q = 1 * .387 * 50
Right?

Answer 8

10^2* my mistake

Answer 9

Or, should I multiply by 3.87 because that's the format it is in my textbook?

Answer 10

use 3.87 * 10^3 since you're dealing with kg

and yes. multiply straight through

Answer 11

If I include the scientific notation, it comes out to 19350, which when simplified, would be 1.935KJ/gC, right?

Answer 12

My next question is this; since object A lost heat (went from 100 to 50 degrees), should my answer be negative?

Answer 13

nvm i do know lol

Answer 14

1.93500*10^3 J/kg C

Answer 15

yes. Q is negative for exothermic reactions

Answer 16

My units will be J/kg*C, because that's how it is in my book.

Just to make sure I'm doing this right, experiment 2 has these stats:

Object A is copper, mass is 3kg, start temp is 100 degrees C, final temp is 75 degrees C
Object B is copper, mass is 1kg, start temp is 0 degrees C, final temp is 75 degrees C

For object A,

Q = 3 * (3.97 * 10^2) * -25
Q = -2.9775 J/kg*C

For object B,
Q = 1 * (3.97 * 10^2) * 75
Q = 2.9775 J/kg*C

The reason I didn't add scientific notation (10^3) is because it's already divided by 1000 when I said kg instead of g in the units.

Answer 17

Or, should it be 2.9775 * 10^4 because the actual answer is 29775? I'm just unsure if it's right without the scientific notation.

Answer 18

Q1 should be -2.97750*10^5 J/kgC

idk what value is but you said it was 3.97 * 10^3 J/kgC, you used 10^2

Answer 19

I said that 10^3 was a mistake and it's 10^2.

Answer 20

my bad. then it's -2.9775*10^4 J/kgC

Answer 21

Gotcha. Thank you! I'll do experiment 3 on my own, but I'd like some help with experiment 4 if you have the time, please.

Answer 22

i do

Answer 23

Here's the information for experiment 4:

Object A is aluminum, 1kg, starting temp is 100, final temp at thermal equilibrium is 36.07
Object B is copper, 4kg, starting temp is 0 degrees, final temp at thermal equilibrium is 35.96.

I'm given 30 second time intervals and the temperature of each object at those time intervals. Thermal equilibrium is achieved at 4 minutes.

I'm supposed to find the heat flow at each time interval. I'm given the equation

(delta)Q/(delta)T

and told that it's in units J/s

So, am I supposed to find Q at each time interval for each object? Not sure how to do this one. Here's what I'm told, word for word:

"Use the equation and information below to complete the dQ/dt column of the table for Experiment 4. 1. Heat Flow equations: dQ/dt is in units of J/s 2. Copper rod: K rod = Thermal Conductivity of Rod = 500 Watt/(m•C) A rod = Area of Cross section of the conducting copper rod = 0.002(m²) L rod = Length of the rod = 0.75 (m) Use Equation 1 to calculate the heat flow through the copper rod at each time increment. Create Graph 2: Heat Flow versus Time, using the data from Time Column and Heat Flow Column."

Answer 24

Here are the temperatures at the time intervals

(time: object A; object B)

30 sec: 64.47; 19.99
1 min: 48.67; 28.88
1 min 30 sec: 41.63; 32.83
2 min: 38.51; 34.59
2 min 30 sec: 37.12; 35.37
3 min: 36.56; 35.72
3 min 30 sec: 36.22; 35.88
4 min: 36.07; 35.96

Answer 25

actually i dont know. sorry :C

Answer 26

Thank you for your time anyway! You've been a great help.