Respuesta :
Answer:
24°C
Explanation:
m = Mass of ice = 625 g
Energy the microwave provides
[tex]750\times 6\times 60=270000\ J[/tex]
Latent heat of melting = 334 J/g
Energy required to melt ice
[tex]625\times 334=208750\ J[/tex]
Actual energy
[tex]270000-208750=61250\ J[/tex]
[tex]C_s[/tex] = Heat capacity for water = 4.18 J/g･°C.
Energy required to melt ice will be equal to the heat absorbed
[tex]Q=mC_s\Delta T\\\Rightarrow 61250=625\times 4.18(T_f-0)\\\Rightarrow T_f=\dfrac{61250}{625\times 4.18}+0\\\Rightarrow T_f=23.4449760766\ ^{\circ}C[/tex]
The temperature is 24°C
Answer:
[tex]T_f=23.34^{\circ}C[/tex]
Explanation:
Given:
initial temperature of the ice cube, [tex]T_i=0^{\circ}C[/tex]
mass of the ice cube, [tex]m=625\ g[/tex]
power of heating by the microwave oven, [tex]P=750\ W[/tex]
time duration of heating, [tex]t=6\ min=360\ s[/tex]
specific enthalpy of fusion of ice, [tex]L=6020\ J.mol^{-1}[/tex]
specific heat capacity of ice, [tex]c=4.18\ J.g^{-1}[/tex]
We find the energy supplied by the microwave:
[tex]E=P.t[/tex]
[tex]E=750\times 360[/tex]
[tex]E=270000\ J[/tex]
The energy required by the given mass of ice to melt:
[tex]E_m=L\times\frac{m}{M}[/tex]
where:
M = molecular mass of the water
[tex]E_m=6020\times \frac{625}{18}[/tex]
[tex]E_m=209027.78\ J[/tex]
Remaining heat that is used in increasing the temperature of the melted ice i.e. water of 0°C:
[tex]\Delta E=E-E_m[/tex]
[tex]\Delta E=270000-209027.78[/tex]
[tex]\Delta E=60972.22\ J[/tex]
Now the rise in temperature of water:
From the heat equation,
[tex]\Delta E=Q[/tex]
[tex]\Delta E=m.c.(T_f-T_i)[/tex]
[tex]60972.22=625\times 4.18\times (T_f-0)[/tex]
[tex]T_f=23.34^{\circ}C[/tex] is the final temperature of the water after the given heat input.
