Tomorrow I have my physics exam and I can’t solve this exercise.
“A calorimeter with a heat capacity of 80 J/K contains 200 g of water at an equilibrium temperature of 20 °c. First, 300 g of water at 35 °c are added and then an unknown mass of water at 52°c. What is this mass if the final temperature is 32°C?”
As a first step I wanted to calculate the equilibrium temperature of the colder masses of water, but that already goes wrong because I can’t convert it to Te. The calorimeter should not be neglected:
80 J/K * (Te-293K) + 4186 J/kgK * 0.200 kg * (Te-293K) = 4186 J/kgK * 0.300 kg * (308-Te)
Please let me know how you convert this to Te and also the result (mass of that water) !
thanks in advance
Answer
Hi Dyo,
I only got your question today, your exam is already over. Hopefully you are still reading the answer now.
Your equation is correct: on the left is the energy absorbed by the calorimeter and the 200g of water, on the right is the energy released by the 300g of added water and what one gets is exactly what the other gives.
I’m rewriting your equation, but use the Celsius scale, because we’re only dealing with temperature differences, and they’re the same in both scales, and since we’re only digitizing, I’m also omitting the units.
80(T-20) + 4186.0.2.(T-20) = 4186.0.3.(35 – T)
I develop the parentheses, take all terms with the variable T together and also all terms without T and get the equation
2176.T = 62297 from which follows T=28.67 so the temperature in degrees Celsius.
We now have 0.500 kg of water in the calorimeter at that temperature and add X kg of 52° and a combined temperature of 32° follows.
We again set up the equilibrium equation, as before:
(32 – 28.67).(80 + 0.5 . 4186) = (52 – 32).(X.4186)
Solve for X and you find X=0.086 kg
From now on, remember that when dealing with questions of physics:
1) know the physical meaning of the formulas you write down
2) use your knowledge of mathematics when elaborating
How was your exam actually?
Answered by
Prof. dr. French Cerulus
physics, especially classical theoretical mechanics, electromagnetism, quantum mechanics, history of physics .
Old Market 13 3000 Leuven
https://www.kuleuven.be/
.