(0.04)c(33.7-23.5)+(0.08)c(33.7-39.6) Find C

[Andrei316]

Sorry if the title is against the rules or anything, I just wanted to be specific as possible :P
1. Homework Statement
V_1(Saltwater) = 40g = 0.04kg
V_{2(Hot-Saltwater)} = 80g = 0.08kg
T_i(Saltwater) = 23.5^oc
T_{i(Hot-Saltwater)} = 39.6^oc
T_f = 33.7c

Question: A cup of 40g saltwater is at 23.5c & A cup of 80g saltwater is at 39.6c, Find the specific heat capacity of salt water. **I measured these myself because it was a mini-lab so the specific heat capacity might not be exactly 3.99x10³J.

2. Homework Equations
I asked my grade 11 physics teacher and this could be solved by using Q_LOST + Q_GAINED and Q=mcΔT. I asked my friends and they couldn't figure it out too ;-;

The Attempt at a Solution

I tried using everything and did anything I could do ...but I still couldn't get the answer of 3.99x10³J. I can easily figure it out if I was it was 2 different substances and at least one heat capacity, but finding only c because they are both salt water confuses me.
m₁cΔT₁ + m₁cΔT₁
(0.04)c(33.7-23.5)+(0.08)c(33.7-39.6)

 

[mfb]

Without a reference (known input heat or something with a known heat capactiance), the whole approach cannot work. You are comparing salt water with salt water.

 

[Andrei316]

Without a reference (known input heat or something with a known heat capactiance), the whole approach cannot work. You are comparing salt water with salt water.

Oh alright, yeah I just wanted to make sure it wasn't possible. My teacher does this thing when he tricks us to check if we actually do our work... it's really annoying but he does teach us why it's impossible and stuff like that. Thanks for your help and time :)

 

[mfb]

You can check the numbers for consistency: Check if the mixing temperature is right.