anonymous
  • anonymous
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?
Mathematics
jamiebookeater
  • jamiebookeater
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Owlfred
  • Owlfred
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anonymous
  • anonymous
wow, this one is thermodynamics right?
anonymous
  • anonymous
yes

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anonymous
  • anonymous
its actually physics but it's considered to be in the math category so i need a lot of help with this.
anonymous
  • anonymous
The heat associated with a certain mass changing temperature is
anonymous
  • anonymous
m*c*(dT)
anonymous
  • anonymous
the energy change in the water has to equal the energy change in the metal
anonymous
  • anonymous
Qm=140*c*(70-10) Qw=220*4.186*(10-0)
anonymous
  • anonymous
you set the two equal to each other and solve for c. That equation will give units of Joule/(gram Celsius)
anonymous
  • anonymous
so would i be solving the equation that you suggested i'm confused
anonymous
  • anonymous
Have you learned the heat/energy required to change the temperature of a substance?
anonymous
  • anonymous
no i don't quite understand how to solve problems like these.
anonymous
  • anonymous
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.
anonymous
  • anonymous
the magnitude of the heat has to be the same for both the metal and the water
anonymous
  • anonymous
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.
anonymous
  • anonymous
The magnitude of the heat is the same in both due to conservation of energy
anonymous
  • anonymous
so basically what would be the numbers in the equation to plug into the problem if is the same.
anonymous
  • anonymous
Your final equation would look like: 140*c*(70-10)=220*4.186*(10-0) 140*60*c=220*10*4.186
anonymous
  • anonymous
and you want to find c in J/gC
anonymous
  • anonymous
so how would i find c
anonymous
  • anonymous
140*60*c=220*10*4.186 8400*c=9209.2 c=9209.2/(8400) c=1.1 J/gC
anonymous
  • anonymous
1.0963 would be c
anonymous
  • anonymous
yeah
anonymous
  • anonymous
so what units should i use for this problem?
anonymous
  • anonymous
that c is J/(gC) or Joules per gram degree Celsius
anonymous
  • anonymous
the energy in Joules it takes to change the temperature of 1 gram of metal 1 degree celsius
anonymous
  • anonymous
so would this be the same as 1.0963 cal/g degree Celsius ?
anonymous
  • anonymous
no 1 cal= 4.186 Joules
anonymous
  • anonymous
if you want calories divide your answer by 4.186
anonymous
  • anonymous
i don't think my answer is right
anonymous
  • anonymous
i have 0.2619
anonymous
  • anonymous
yep I think that's good
anonymous
  • anonymous
why dont you think it is right
anonymous
  • anonymous
i don't know because i think that my units wont match up with the right answer that i just put up there
anonymous
  • anonymous
im not sure what you mean
anonymous
  • anonymous
like should it say 0.2619 cal/g degrees Celsius, does that sound right?
anonymous
  • anonymous
oh yeah those are the units for specific heat
anonymous
  • anonymous
thank you so much I got it right thanks
anonymous
  • anonymous
you're welcome :)

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