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Sagot :
Answer:
1.06 °C
Explanation:
From the question given above, the following data were obtained:
Mass of gold (M₉) = 10 g
Specific heat capacity of gold (C₉) = 0.129 J/gºC
Initial temperature of gold (T₉) = 24 °C
Mass of water (Mᵥᵥ) = 118 g
Specific heat capacity of water (Cᵥᵥ) = 4.184 J/gºC
Initial temperature of water (Tᵥᵥ) = 1 °C
Equilibrium temperature (Tₑ) =?
The equilibrium temperature of the system can be obtained as follow:
Heat loss by the gold = heat gained by the water
M₉C₉(T₉ – Tₑ) = MᵥᵥCᵥᵥ(Tₑ – Cᵥᵥ)
10 × 0.129 (24 – Tₑ) = 118 × 4.184 (Tₑ – 1)
1.29(24 – Tₑ) = 493.712 (Tₑ – 1)
Clear bracket
30.96 – 1.29Tₑ = 493.712Tₑ – 493.712
Collect like terms
30.96 + 493.712 = 493.712Tₑ + 1.29Tₑ
524.672 = 495.002Tₑ
Divide both side by 495.002
Tₑ = 524.672 / 495.002
Tₑ = 1.06 °C
Therefore, the temperature of the system is 1.06 °C
The amount of heat of the system is measured by a device called a calorimeter. The final temperature of the system will be 1.06 degrees celsius.
What is equilibrium temperature?
The equilibrium temperature is the temperature that follows the law of thermodynamics and is said to be the system that has alike temperatures.
Given,
Mass of Ag [tex]\rm (M_{g})[/tex] = 10g
Specific heat capacity of Ag [tex](\rm C_{g})[/tex] = [tex]\rm 0.129 J/g^{\circ}C[/tex]
The initial temperature of Ag [tex](\rm T_{g})[/tex] = [tex]24 ^{\circ}\;\rm C[/tex]
Mass of water [tex](\rm M_{w})[/tex] = 118 g
Specific heat capacity of water [tex](\rm C_{w})[/tex] = [tex]4.184 \rm \;J/g^{\circ}\;\rm C[/tex]
The initial temperature of water [tex](\rm T_{w})[/tex] = [tex]1 ^{\circ}\;\rm C[/tex]
Equilibrium temperature = [tex](\rm T_{e})[/tex]
The equilibrium temperature can be shown as, heat loss by the gold = heat gained by the water:
[tex]\rm \rm M_{g}C_{g}(T_{g} - T_{e}) = M_{w}C_{w}(T_{e}-C_{w})[/tex]
Substituting values in the equation:
[tex]\begin{aligned} 10 \times 0.129 (24 - \rm T_{e}) &= 118 \times 4.184 (\rm T_{e} - 1)\\\\\rm 1.29(24 - T_{e}) &= 493.712 (\rm T_{e} - 1)\\\\524.672 &= 495.002 \;\rm T_{e}\end{aligned}[/tex]
Now divide both the sides by 495.002:
[tex]\begin{aligned} \rm T_{e} &= \dfrac{524.672 }{495.002}\\\\\rm T_{e} &= 1.06 \;^{\circ}\rm C\end{aligned}[/tex]
Therefore, the final temperature of the system is 1.06 degrees celsius.
Learn more about equilibrium temperature here:
https://brainly.com/question/16207236
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