Answer:
The final equilibrium temperature is approximately 26.69 °C
Step-by-step explanation:
The heat transferred, ΔQ, from a hot body to a cold one is given by the following formula;
ΔQ = m·c·ΔT
Where;
m = The mass of the body
c = The specific heat capacity of the body
ΔT = The temperature change of the body
The given mass of the gold bar, m₁ = 20.0 kg
The initial temperature of the gold bar, T₁ = 35.0 °C
The specific heat capacity of gold, c₁ = 0.13 kJ/(kg·K)
The mass of the glass container, m₂ = 0.8 kg
The initial temperature of the glass container, T₂ = 15°C
The specific heat capacity of glass, c₂ = 0.792 kJ/(kg·K)
The mass of the added water, m₃ = 2.0 kg
The initial temperature of the added water, T₃ = 25°C
The specific heat capacity of water, c₃ = 4.2 kJ/(kg·K)
The heat lost by the gold = The heat gained by the glass and the water
Let 'T' represent the temperature at the final equilibrium, we have;
m₁·c₁·ΔT₁ = m₂·c₂·ΔT₂ + m₃·c₃·ΔT₃
Where;
ΔT₁ = T₁ - T
ΔT₂ = T - T₂
ΔT₃ = T - T₃
∴ 20.0 × 0.13 × (35 - T) = 0.8 × 0.792 × (T - 15) + 2.0 × 4.2 × (T - 25)
Expanding and collecting like terms (using a graphing calculator) gives;
91 - 2.6·T = 9.0336·T - 219.504
9.0336·T + 2.6·T = 219.504 + 91 = 310.504
11.6336·T = 310.504
T = 310.504/11.6336 ≈ 26.69
The final equilibrium temperature, T ≈ 26.69 °C.