Answer to Question #170144 in Molecular Physics | Thermodynamics for Seun Olabanji

Question #170144

35g of water at 0 degree Celsius is completely converted to ice at 0 degree Celsius by extracting 2 kilo joules of heat from it. If the specific heat capacity of water is 4200 joules per kilogram per Kelvin, calculate the specific latent heat of fusion of ice


1
Expert's answer
2021-03-09T15:27:07-0500

The amount of heat extracting from the water can be written as follows:


Q=Q1+Q2,Q=Q_1+Q_2,

here, Q1Q_1 is the amount of heat that should be extracted to cool the water from 10C10^{\circ}C to 0C0^{\circ}C, Q2Q_2 is the amount of heat that should be extracted to convert water from 0C0^{\circ}C to ice at 0C0^{\circ}C.

Then, we can write:


Q=mcΔT+mLf.Q=mc\Delta T+mL_f.

From this equation we can find the specific latent heat of fusion of ice:


Lf=QmcΔTm,L_f=\dfrac{Q-mc\Delta T}{m},L_f=\dfrac{2\cdot10^3\ J-0.035\ kg\cdot4200\ \dfrac{J}{kg\cdot \!^{\circ}C}\cdot10^{\circ}C}{0.035\ kg}=1.5\cdot10^4\ \dfrac{J}{kg}.

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