Question

Physical therapists know as you soak tired muscles in a hot tub, the water will cool down as you heat up. If a 67.9 person at 37.1 oC immerses in 50.2 kg of water at 40.5o C, the equilibrium temperature is 38.7 oC. What is the specific heat of the person? Use 4.186 kJ/kgoC for the specific heat of water. Answer to 3 significant figures in kJ/kgoC .

Answer 1

the \[\large m c \Delta T\]will be equal for both the person and the water

Answer 2

I got 3.47

Answer 3

I didn't work out the answer; show your work.

Well the heat lost by one equals the heat gained by the other: \[\large m_p c_p \Delta T_p=-m_w c_w \Delta T_w\]
left side is the person, right side is the water

Answer 4

Ok lemme try it again..

Answer 5

How come there's a negative??

Answer 6

"heat lost by one equals the heat gained by the other"
lost heat is negative.

but you don't really need it. As long as both sides are positive.

Answer 7

Oh ok. So would I multiply those out?

Answer 8

Plug in all the relevant numbers

Answer 9

Ok Idk. I'm kinda confused. There's alot of numbers to deal with. This is wht I have:
67.9(50.2) = 40.5(38.7)
I really don't know what I'm doing. c= capacity right??

Answer 10

Start with the left then. What the mass of the person, and the change in temp for the person? Leave their specific heat as c.

On the right. What is the mass of water, the c for the water, and the change in temp for the water.

Answer 11

First you might want to work out the change in temperature for the water and person.

Answer 12

Ok this is wht I have:
67.9(37.1)(??) = 50.2(40.5)(38.7)
Does that look right?

Answer 13

Slow down. Make sure you have the numbers BEFORE plugging things in.

Person:
mass:
initial temp:
final temp:
specific heat:

Water:
mass:
initial temp:
final temp:
specific heat:

Keep in mind the equilibrium temp is the final temp (for both, since they both reach it)

Answer 14

so:
M: 67.9kg
IT: 37.1 Celcius
FT: 38.7

WATER:
M: 550.2kg
IT: 40.5
FT: 38.7
???

Answer 15

Yes but you forgot c for the person, and 4.186 for the water

Now work out the change in temp for each. Plug it all into the equation.

Answer 16

Well I do not see the c for the person

Answer 17

That's because it's what you're solving for

Answer 18

That's why i said to use c for it.

Answer 19

Thanks! Figured it out.

Answer 20

You're welcome, good job.

Answer 21

Yea. I got 3.48.

Answer 22

Looks right.