Question

An insulated thermos contains 102.0 cm3 of hot coffee at a temperature of 80.0 °C. You...

An insulated thermos contains 102.0 cm3 of hot coffee at a temperature of 80.0 °C. You put in 14.0 g of ice cube at its melting point to cool the coffee. What is the temperature of the coffee once the ice has melted and the system is in thermal equilibrium? Treat the coffee as though it were pure water. (Answer in °C)

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Answer #1

Lf = specific latent heat of fusion of ice = 334,000J/kg (energy to melt 1kg of ice at 0degC)
Heat supplied to melt ice = m_ice x Lf = 0.0140 x 334000 = 4676J

Final temp = T deg C
Heat lost by coffee cooling from 80degC to T = m.c.delta_T = 0.080 x 4200 x (80 - T)
Heat gained by water from melted ice being raised from 0degC to T = m.c.delta_T
= 0.014 x 4200 x (T - 0)
______________________________________...
Heat lost by cofee = Heat needed to melt ice + Heat needed to rais melted ice from 0degC to T
0.080 x 4200 x (80 - T) = 4676 + 0.014 x 4200 x T

26880-336T=58.8T+4676

394.8T=22204

T=56.24 C

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