An ice chest at a beach party contains 12 cans of soda at 3.05 °C. Each can of soda has a mass of 0.35 kg and a specific heat capacity of 3800 J/(kg C°). Someone adds a 7.15-kg watermelon at 25.0 °C to the chest. The specific heat capacity of watermelon is nearly the same as that of water. Ignore the specific heat capacity of the chest and determine the final temperature T of the soda and watermelon in degrees Celsius.
heat lost + heat gained = 0
mcdeltaT + mcdeltaT = 0
substitute Tf - Ti for delta T (in both cases). Tf is final T and Ti is initial T. Solve for Tf. Post your work if you get stuck.
Jena: Please don't change names on us. We try to get to know what kind of errors each student is making in order to effectively instruct. Changing names messes that up.
Thanks.
The sum of the heat gains is zero (one will gain heat, the other lose (negative gain)).
0=heatwatermelon gained + heatsodagained
0=masswatermellon*c*(Tf-25) + 12*.35*csoda*(Tf-3.05)
solve for Tf.
(.35)(3800)(Tf-3.05)+(7.15)(4186)(Tf-25)=0
OK but how do I get the Tf for both in the same time
I am Jena's sister
Sorry if I made an error.bobpursley
You haven't multiplied 0.35 kg/can x 12 cans = ?? kg soda.
Just do algebra and the Tf will be the only unknown in the equation.
I am stuck I got a whole different #.
12*0.35*3800*(Tf-3.05) + 7.15*4186*(Tf-25.0)=0
15960Tf - 48678 + 29929.9Tf - 748247.5 = 0
Solve for Tf. I assume you can take it from here.
To solve for Tf, use algebra to slove for unknowns.
Try this:
(12)(0.35)(3800)(5)+(7.15)(4186)(25)/(12)(0.35)(3800)+(7.5)(4186)
and what's left over is the answer for your unknown
I input the wrong temp of the soda can so just replace the (5) with (3.05) nd that will work
To solve for Tf, we need to combine like terms on the left side of the equation:
15960Tf + 29929.9Tf - 48678 - 748247.5 = 0
Combining the terms:
45989.9Tf - 796925.5 = 0
Next, we move the constant term to the other side of the equation:
45989.9Tf = 796925.5
Now, divide both sides of the equation by 45989.9 to isolate Tf:
Tf = 796925.5 / 45989.9
Calculating this, we find:
Tf ≈ 17.33 °C
So, the final temperature of the soda and watermelon in the ice chest is approximately 17.33 °C.
To solve for Tf, we need to simplify the equation and isolate the term with Tf. Let's continue with the calculation:
12*0.35*3800*(Tf-3.05) + 7.15*4186*(Tf-25.0) = 0
15960Tf - 48678 + 29929.9Tf - 748247.5 = 0
Combining like terms:
45989.9Tf - 796925.5 = 0
Now, let's isolate the term with Tf:
45989.9Tf = 796925.5
Dividing both sides by 45989.9:
Tf = 17.32
Therefore, the final temperature (Tf) of the soda and watermelon will be approximately 17.32 °C.