## 818jasmine 4 years ago when a 140g piece of metal at 70 degree Celsius is placed in 220g of water at 0 degree Celsius, the metal is cooled, and the water is warmed and both come to a final temperature of 10 degree Celsius. What is the specific heat of the metal?

1. Owlfred

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2. Ms.bio

wow, this one is thermodynamics right?

3. 818jasmine

yes

4. 818jasmine

its actually physics but it's considered to be in the math category so i need a lot of help with this.

5. rsvitale

The heat associated with a certain mass changing temperature is

6. rsvitale

m*c*(dT)

7. rsvitale

the energy change in the water has to equal the energy change in the metal

8. rsvitale

Qm=140*c*(70-10) Qw=220*4.186*(10-0)

9. rsvitale

you set the two equal to each other and solve for c. That equation will give units of Joule/(gram Celsius)

10. 818jasmine

so would i be solving the equation that you suggested i'm confused

11. rsvitale

Have you learned the heat/energy required to change the temperature of a substance?

12. 818jasmine

no i don't quite understand how to solve problems like these.

13. rsvitale

ok we have the equation Q=mc(dT) where Q is heat, m is mass of whatever is changing temperature, dT is the change in Temperature.

14. rsvitale

the magnitude of the heat has to be the same for both the metal and the water

15. rsvitale

so you plug the known values into the heat equation for water and metal and set them equal to each other to find the specific heat you are looking for.

16. rsvitale

The magnitude of the heat is the same in both due to conservation of energy

17. 818jasmine

so basically what would be the numbers in the equation to plug into the problem if is the same.

18. rsvitale

Your final equation would look like: 140*c*(70-10)=220*4.186*(10-0) 140*60*c=220*10*4.186

19. rsvitale

and you want to find c in J/gC

20. 818jasmine

so how would i find c

21. rsvitale

140*60*c=220*10*4.186 8400*c=9209.2 c=9209.2/(8400) c=1.1 J/gC

22. 818jasmine

1.0963 would be c

23. rsvitale

yeah

24. 818jasmine

so what units should i use for this problem?

25. rsvitale

that c is J/(gC) or Joules per gram degree Celsius

26. rsvitale

the energy in Joules it takes to change the temperature of 1 gram of metal 1 degree celsius

27. 818jasmine

so would this be the same as 1.0963 cal/g degree Celsius ?

28. rsvitale

no 1 cal= 4.186 Joules

29. rsvitale

30. 818jasmine

i don't think my answer is right

31. 818jasmine

i have 0.2619

32. rsvitale

yep I think that's good

33. rsvitale

why dont you think it is right

34. 818jasmine

i don't know because i think that my units wont match up with the right answer that i just put up there

35. rsvitale

im not sure what you mean

36. 818jasmine

like should it say 0.2619 cal/g degrees Celsius, does that sound right?

37. rsvitale

oh yeah those are the units for specific heat

38. 818jasmine

thank you so much I got it right thanks

39. rsvitale

you're welcome :)