I really really need help w/this problem I think i figured it out but i have to be sure i did it right in order to do others similar to it
please help
thanks
Metal Specific Heat (J/g-C)
Al (s) 0.900
Au(s) 0.129
Cu(s) 0.385
Fe(s) 0.444
Hg(l) 0.139
H2O(l) 4.184
C2H5OH(l) 2.46
A piece of metal at a temp of 95.0oC and a mass of 67.0 g is dropped into a beaker of water containing 100 g at a temp. of 30.0oC. If the final temperature reached is 42.7.0oC, what is the identity of the metal?
the sum of the heats gained is zero.
heatgainedmetal+heatgainedwater=0
95*cm*(30-95)=100*4.18(42.7-30)
1.28
would it be Au?
I don't think so.
I think the 95 you have listed should be 67 g (at least from the post) and delta T for the metal is (Tfinal-Tintial). The final T from the problem is 42.7 and the initial is 95 isn't it? Check your numbers in the post. That may be a typo.
To solve this problem, we need to use the principle of heat transfer. The heat gained by the metal is equal to the heat lost by the water. We can use the formula:
(q metal) + (q water) = 0
where q represents the heat gained or lost.
The heat gained by the metal is given by:
(q metal) = mass metal * specific heat metal * change in temperature
The heat lost by the water is given by:
(q water) = mass water * specific heat water * change in temperature
From the given data, we can see that the specific heat of gold (Au) is 0.129 J/g-C. So, we can substitute the values into the equation:
(mass metal) * (specific heat metal) * (final temperature - initial temperature) + (mass water) * (specific heat water) * (final temperature - initial temperature) = 0
Let's solve this equation step by step.
Given values:
mass metal = 67.0 g
specific heat metal = 0.129 J/g-C
initial temperature of metal = 95.0oC
mass water = 100 g
specific heat water = 4.184 J/g-C
initial temperature of water = 30.0oC
final temperature = 42.7oC
Substituting the values into the equation:
(67.0 g) * (0.129 J/g-C) * (42.7oC - 95.0oC) + (100 g) * (4.184 J/g-C) * (42.7oC - 30.0oC) = 0
Now, let's perform the calculations:
(-0.558) + (526.60) = 0
Since the sum is not equal to zero, our initial assumption that the heat gained and lost are equal is incorrect, and our calculation is wrong. Therefore, Au cannot be the identity of the metal based on the given data.
To find the correct identity of the metal, we would need additional information such as the final temperature reached and the specific heat capacity of the metal.