Respuesta :
Answer:
The new water temperature is 26.4 °C
Explanation:
Given;
mass of copper, [tex]M_{cu}[/tex] = 26 g = 0.026 kg
temperature of copper, t = 300 °C
volume of water, V = 120 mL = 0.12 L
temperature of water, t = 21 °C
density of water, ρ = 1 kg/L
mass of water = density x volume
mass of water = (1 kg/L) x 0.12 L = 0.12 kg
heat lost by copper = heat gained by water
Both copper and water reach final temperature, T
Heat gained by water, [tex]Q_w[/tex] = [tex]m_w[/tex]cΔθ = [tex]m_w C(T - t)[/tex]
[tex]Q_w = m_w C(T - t)\\\\Q_w = 0.12*4200(T-21)\\\\Q_w = 504(T-21)[/tex]
Heat lost by copper is given by;
[tex]Q_{cu} = m_{cu}C(300-T)\\\\Q_{cu} = 0.026*385(300-T)\\\\Q_{cu} = 10.01(300 - T)[/tex]
[tex]Q_{cu} = Q_w[/tex]
504(T- 21) = 10.01(300 - T)
504 T - 10584 = 3003 - 10.01 T
504 T + 10.01 T= 3003 + 10584
514.01 T = 13587
T = (13587) / 514.01
T = 26.4 °C
Therefore, the new water temperature is 26.4 °C
The new water temperature using the given parameters is;
26.49°C
We are given;
Mass of copper; m_cu = 26 g = 0.026 kg
Temperature; T_cu = 300 °C
Volume of water; V = 120 mL = 0.12 L
Temperature of water, T_w = 21 °C
Density of water; ρ = 1 kg/L
Let us find the mass of water from the formula;
m_w = ρ × V
m_w = 1 × 0.12
m_w = 0.12 kg
Now, from the principle of conservation of energy, we can say that the total heat lost by a hot body is equal to the total heat gained by a cold body.
The hot body here is copper while the cold body is water. Thus;
Heat lost by copper = Heat gained by water
Formula for heat lost by copper is;
Q_cu = m_cu * c_cu * (T_f - T_cu)
Formula for heat gained by water is;
Q_w = m_w * c_w * (T_f - T_w)
Where;
T_f is final temperature reached by copper and water
c_cu is specific heat capacity of copper = 385 J/kg.°C
c_w is specific heat capacity of water = 4200 J/kg.°C
Thus;
Q_cu = 0.026 × 385 × (300 - T_f)
Q_cu = 3030 - 10.01T_f
similarly;
Q_w = 0.12 × 4200 × (T_f - 21)
Q_w = 504T_f - 10584
Thus;
3030 - 10.01T_f = 504T_f - 10584
3030 + 10584 = 504T_f + 10.01T_f
13614 = 514.01T_f
T_f = 13614/514.01
T_f = 26.49°C
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