Respuesta :
Answer:
The final temperature will be 26.7 °C
Explanation:
Step 1: Data given
Mass of the piece granite = 1.10 kg
Specific heat = 0.803 J/g°C
Initial temperature = 87.3 °C
Volume of water = 2.00 L
Initial temperature of water = 20.3°C
Step 2:Calculate the final temperature
Heat lost by granite = heat won by water
Qgranite = -Qwater
Q = m*c*ΔT
m(granite) * c(granite) * ΔT(granite) = -m(water) * c(water) * ΔT(water)
⇒ mass of granite = 1100 grams
⇒ c(granite) = 0.803 J/g°C
⇒ ΔT(granite) = T2 - T1 = T2 - 87.3
⇒ mass of water = 2000 grams
⇒ c(water) = 4.184 J/g°C
⇒ΔT(water) = T2 - 20.3 °C
1100 *0.803 * (T2 - 87.3) = -2000 * 4.184 * (T2 - 20.3)
883.3(T2 - 87.3) = -8368 (T2- 20.3)
883.3T2 - 77112.09 = -8368T2 + 169870.4
883.3T2 + 8368T2 = 169870.4 +77112.09
9251.3T2 = 246982.49
T2 = 26.7 °C
The final temperature will be 26.7 °C
The final temperature of the granite and the water will be 26.6 °C.
Heat energy
In a mixture between two substances of different temperatures, there is heat transfer, in which the one with a lower temperature receives this heat and the one with a higher temperature loses the heat.
In a system, the value of heat lost and received is equal.
This heat is represented by the following expression:
[tex]Q = m \times c \times T[/tex]
The value of heat is given in calories, the value of temperature is given in celsius and the value of mass is given in grams
Thus, to find the value of the final temperature of the mixture, it is enough to equate the heat of the two substances.
[tex]1100 \times (\frac{0.803}{4,18}) \times (t_{f} - 83.7) = 2000 \times 1 \times (t_{f} - 20.3)[/tex]
[tex]220 (t_{f} - 83.7) = 2000 (t_{f} - 20.3)[/tex]
As the value of the granite final temperature is lower than the initial temperature, the result of the temperature variation would be negative, so the signs of the expression can be changed.
[tex]18414 - 220 t_{f} = 2000 t_{f} - 40600[/tex]
[tex]2220 t_{f} = 59,014[/tex]
[tex]t_{f} = 26.6[/tex]
So, the final temperature of the granite and the water will be 26.6 °C.
Learn more about heat energy in: brainly.com/question/1495272
