Using heat exchange and conservation of thermal energy, determine the specific heat capacity for your metal.
So the data we have is:
Aluminium:
Mass - 0.004
Initial temp - 100C
Final temp: 32C
Water:
Mass -0.1
Initial temp - 20C
Final temp - 32C
I know that the formula is mct = mct but I don't get what I'm solving for or how to do it.
Thank you for your help!
assuming kilograms (please specify units)
water is 4180 J/(kg deg C)
heat into water = (0.1)4180*(32-20)
Al is C J/(kg deg C)
heat out od Al = .004(C)(100-32)
so
.004(C)(100-32)=(0.1)4180*(32-20)
Thank you for answering! So when I did the math I got 18,441 j/kg degree c
However the actual value is supposed to be 900.did I do the math wrong or did I just do something wrong in the experiment? Thanks!
To determine the specific heat capacity of the metal, we can use the principle of heat exchange and conservation of thermal energy. The formula you mentioned, mct = mct, represents the conservation of thermal energy, where m represents the mass, c is the specific heat capacity, and t stands for the change in temperature.
In this case, we have two substances: aluminium (metal) and water. The subscript "a" will represent aluminium, and "w" will represent the water.
The conservation of thermal energy equation can be written as:
ma * ca * Δta = mw * cw * Δtw
Here, ma is the mass of aluminium, ca is the specific heat capacity of aluminium, Δta is the change in temperature of aluminium, mw is the mass of water, cw is the specific heat capacity of water, Δtw is the change in temperature of water.
Plugging in the given data into the equation:
ma * ca * (Ti - Tf)a = mw * cw * (Ti - Tf)w
where Ti is the initial temperature and Tf is the final temperature.
For aluminium:
ma = 0.004 kg
(Ti - Tf)a = 100 - 32 = 68°C
For water:
mw = 0.1 kg
(Ti - Tf)w = 20 - 32 = -12°C
Now, rearranging the equation for specific heat capacity of aluminium (ca):
ca = (mw * cw * (Ti - Tf)w) / (ma * (Ti - Tf)a)
Plugging in the values:
ca = (0.1 kg * 4,186 J/kg°C * -12°C) / (0.004 kg * 68°C)
Simplifying this equation will give you the specific heat capacity of the aluminium.
Remember to convert the temperatures to Kelvin if necessary. Also, make sure you use consistent units (e.g., grams or kilograms, Celsius or Kelvin) for accurate results.