Answer :
To determine the final temperature of the coffee after all of the ice melts, we can use the principle of conservation of energy. The temperature of the coffee, after all of the ice melts, is approximately 116.94°C.
The energy lost by the coffee when it cools down is equal to the energy gained by the ice when it melts. We can calculate these energies using the formulas:
Q_lost = m_coffee * c_water * ΔT_coffee
Q_gained = m_ice * ΔH_fusion
where:
Q_lost is the energy lost by the coffee (in Joules),
m_coffee is the mass of the coffee (in grams),
c_water is the specific heat capacity of water (4.18 J/g°C),
ΔT_coffee is the change in temperature of the coffee (from initial to final),
Q_gained is the energy gained by the ice (in Joules),
m_ice is the mass of the ice (in grams), and
ΔH_fusion is the enthalpy of fusion of water (334 J/g).
We can set these two energies equal to each other and solve for ΔT_coffee:
m_coffee * c_water * ΔT_coffee = m_ice * ΔH_fusion
Plugging in the given values:
195 g * 4.18 J/g°C * ΔT_coffee = 51.7 g * 334 J/g
Simplifying the equation:
815.1 ΔT_coffee = 17223.8
ΔT_coffee = 17223.8 / 815.1
ΔT_coffee ≈ 21.14°C
The change in temperature of the coffee is approximately 21.14°C. To find the final temperature, we add this change to the initial temperature of the coffee:
Final temperature = 95.8°C + 21.14°C
Final temperature ≈ 116.94°C
Therefore, the temperature of the coffee after all of the ice melts is approximately 116.94°C.
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