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?

- anonymous

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- anonymous

wow, this one is thermodynamics right?

- anonymous

yes

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## More answers

- anonymous

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

- anonymous

The heat associated with a certain mass changing temperature is

- anonymous

m*c*(dT)

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- 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

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

- 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

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

- anonymous

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

- anonymous

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

- anonymous

and you want to find c in J/gC

- anonymous

so how would i find c

- anonymous

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

- anonymous

1.0963 would be c

- anonymous

yeah

- anonymous

so what units should i use for this problem?

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

no 1 cal= 4.186 Joules

- anonymous

if you want calories divide your answer by 4.186

- anonymous

i don't think my answer is right

- anonymous

i have 0.2619

- anonymous

yep I think that's good

- anonymous

why dont you think it is right

- 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

im not sure what you mean

- anonymous

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

- anonymous

oh yeah those are the units for specific heat

- anonymous

thank you so much I got it right thanks

- anonymous

you're welcome :)

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