Respuesta :
Answer:
The time required to melt the frost is 3.25 hours.
Explanation:
The time required to melt the frost dependes on the latent heat of the frost and the amount of heat it is transfered by convection to the air .
The heat transferred per unit area can be expressed as:
[tex]q=h_c*A*\Delta T\\\\q/A=h_c*\Delta T[/tex]
being hc the convective heat transfer coefficient (2 Wm^-2K^-1) and ΔT the difference of temperature (20-0=20 °C or K).
[tex]q/A=h_c*\Delta T=2\frac{W}{m^2K}*20K=40\frac{W}{m^2}[/tex]
If we take 1 m^2 of ice, with 2 mm of thickness, we have this volume
[tex]V=T*A = 0.002 m * 1 m^2=0.002m^3[/tex]
The mass of the frost can be estimated as
[tex]M=\rho * V=700\frac{kg}{m^3}*0.002m^3= 1.4 kg[/tex]
Then, the amount of heat needed to melt this surface (1 m²) of frost is
[tex]Q=L*M=334\frac{kJ}{kg}*1.4kg= 467.6kJ[/tex]
The time needed to melt the frost can be calculated as
[tex]t=\frac{Q}{(q/A)}=\frac{467.6kJ/m2}{40W/m2} = 11.69\frac{kJ}{W}*\frac{1W*s}{1J}*\frac{1000J}{1kJ}= 11690s=3.25h[/tex]
