818jasmine
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?
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Owlfred
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Ms.bio
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wow, this one is thermodynamics right?
818jasmine
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yes
818jasmine
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its actually physics but it's considered to be in the math category so i need a lot of help with this.
rsvitale
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The heat associated with a certain mass changing temperature is
rsvitale
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m*c*(dT)
rsvitale
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the energy change in the water has to equal the energy change in the metal
rsvitale
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Qm=140*c*(70-10)
Qw=220*4.186*(10-0)
rsvitale
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you set the two equal to each other and solve for c. That equation will give units of Joule/(gram Celsius)
818jasmine
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so would i be solving the equation that you suggested i'm confused
rsvitale
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Have you learned the heat/energy required to change the temperature of a substance?
818jasmine
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no i don't quite understand how to solve problems like these.
rsvitale
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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.
rsvitale
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the magnitude of the heat has to be the same for both the metal and the water
rsvitale
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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.
rsvitale
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The magnitude of the heat is the same in both due to conservation of energy
818jasmine
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so basically what would be the numbers in the equation to plug into the problem if is the same.
rsvitale
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Your final equation would look like:
140*c*(70-10)=220*4.186*(10-0)
140*60*c=220*10*4.186
rsvitale
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and you want to find c in J/gC
818jasmine
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so how would i find c
rsvitale
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140*60*c=220*10*4.186
8400*c=9209.2
c=9209.2/(8400)
c=1.1 J/gC
818jasmine
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1.0963 would be c
rsvitale
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yeah
818jasmine
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so what units should i use for this problem?
rsvitale
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that c is J/(gC) or Joules per gram degree Celsius
rsvitale
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the energy in Joules it takes to change the temperature of 1 gram of metal 1 degree celsius
818jasmine
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so would this be the same as 1.0963 cal/g degree Celsius ?
rsvitale
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no 1 cal= 4.186 Joules
rsvitale
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if you want calories divide your answer by 4.186
818jasmine
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i don't think my answer is right
818jasmine
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i have 0.2619
rsvitale
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yep I think that's good
rsvitale
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why dont you think it is right
818jasmine
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i don't know because i think that my units wont match up with the right answer that i just put up there
rsvitale
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im not sure what you mean
818jasmine
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like should it say 0.2619 cal/g degrees Celsius, does that sound right?
rsvitale
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oh yeah those are the units for specific heat
818jasmine
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thank you so much I got it right thanks
rsvitale
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you're welcome :)