Question

Calculate the change in entropy when 1.00 kg of water at 100 degree C is vaporized and converted to steam at 100 degree C. Assume that the heat of vaporization of water is 2256 Times 103 J/kg. Calculate the change in entropy when 1.00 kg of ice is melted at 0 degree C. Assume that the heat of fusion of water is Lf = 3.34 Times 105J/kg. Is the change entropy greater for melting or for vaporization? the change entropy greater for melting the change entropy greater for vaporization

Answer 1

Answer:

Case 1 : Entropy of vaporization of water is $\Delta S=6.048 \times 10^{3}$

Case 2 :Entropy of fusion of ice is $\Delta S=1.2234 \times 10^{3}$

Result : Entropy of vaporization of water is greater than entropy of fusion of ice

Explanation:

Entropy of closed system is given by $\Delta S=\frac{\Delta Q}{T}$

Where $\Delta S$ is change of entropy, $\Delta Q$ is change of heat and T is absolute temperature in kelvin

Case 1 : During vaporization of water

It is said that " 1.00 kg of water at 100 degree C is vaporized and converted to steam at 100 degree C"

Given Heat of vaporization of water is $2256 \times 10^{3}$ J/kg.

$\Delta Q = mL$

m=1 kg of water

L=$2256 \times 10^{3}$ J/kg.

$\Delta Q = mL = 2256 \times 10^{3}$

Entropy of closed system is given by $\Delta S=\frac{\Delta Q}{T}$

Where, T=100+273=373K

$\Delta S=\frac{ 2256 \times 10^{3}}{373}$

$\Delta S=6.048 \times 10^{3}$

Thus, Entropy of vaporization of water is $\Delta S=6.048 \times 10^{3}$

Case 2 : During fusion of ice

It is said that " 1.00 kg of ice at 0 degree C is melted and converted to water at 0 degree C"

Given Heat of fusion of ice is $3.34 \times 10^{5}$ J/kg.

$\Delta Q = mL$

m=1 kg of ice

L=$3.34 \times 10^{5}=334 \times 10^{3} J/kg.[tex]\Delta Q = mL = 334 \times 10^{3}$

Entropy of closed system is given by $\Delta S=\frac{\Delta Q}{T}$

Where, T=0+273=273K

$\Delta S=\frac{ 334 \times 10^{3}}{373}$

$\Delta S=1.2234\times 10^{3}$

Thus, Entropy of fusion of ice is $\Delta S=1.2234 \times 10^{3}$

Therefore, Entropy of vaporization of water is greater than entropy of fusion of ice