Question 320: Thermodynamics & KTG

Question

An ice cube of dimensions $$60 \mathrm{~cm} 	imes 50 \mathrm{~cm} 	imes 20 \mathrm{~cm}$$ is placed in an insulation box of wall thickness $$1 \mathrm{~cm}$$. The box keeping the ice cube at $$0^{\circ} \mathrm{C}$$ of temperature is brought to a room of temperature $$40^{\circ} \mathrm{C}$$. The rate of melting of ice is approximately :
(Latent heat of fusion of ice is $$3.4 	imes 10^{5} \mathrm{~J} \mathrm{~kg}^{-1}$$ and thermal conducting of insulation wall is $$0.05 \,\mathrm{Wm}^{-1 \circ} \mathrm{C}^{-1}$$ )

Accepted Answer

$${{\Delta Q} \over {\Delta t}} = {{kA({T_1} - {T_2})} \over l}$$
$$ \Rightarrow {{mL} \over {\Delta t}} = {{kA({T_1} - {T_2})} \over l}$$
$$ \Rightarrow {m \over {\Delta t}} = {{kA({T_1} - {T_2})} \over {Ll}}$$
$$ \simeq 61.1 	imes {10^{ - 5}}$$ kg/s

Answer

$$61 	imes 10^{-3} \mathrm{~kg} \mathrm{~s}^{-1}$$

Answer

$$61 	imes 10^{-5} \mathrm{~kg} \mathrm{~s}^{-1}$$

Answer

$$208 \mathrm{~kg} \mathrm{~s}^{-1}$$

Answer

$$30 	imes 10^{-5} \mathrm{~kg} \mathrm{~s}^{-1}$$

Thermodynamics & KTG

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