Question

904.5 g of ice is melted at a temperature of
29◦F.
Find the change in entropy.
Answer in units of J/K.

Answer 1

Answer on Question 59904, Physics, Molecular Physics, Thermodynamics

Question:

904.5 g of ice is melted at a temperature of 29°F. Find the change in entropy. Answer in units of J/K.

Solution:

First of all, let's convert Fahrenheit to Kelvin:

$$T_{(K)} = \left(T_{(0\text{F})} + 459.67\right) \cdot \frac{5}{9} = (29{}^{\circ}\text{F} + 459.67) \cdot \frac{5}{9} = 271.5\ \text{K}.$$

We can find the change in entropy from the formula:

$$\Delta S = \frac{Q}{T},$$

here, $Q$ is the amount of heat needed to melt the ice, $T$ is the temperature.

Let's find the amount of heat needed to melt the ice:

$$Q = m_{ice} L_f,$$

here, $m_{ice}$ is the mass of ice, $L_f = 3.33 \cdot 10^5\ \text{J/kg}$ is the latent heat of fusion of ice.

Finally, we can calculate the change in entropy:

$$\Delta S = \frac{Q}{T} = \frac{m_{ice} L_f}{T} = \frac{0.9045\ \text{kg} \cdot 3.33 \cdot 10^5\ \frac{\text{J}}{\text{kg}}}{271.5\ \text{K}} = 1109.4\ \frac{\text{J}}{\text{K}}.$$

Answer:

$$\Delta S = 1109.4\ \frac{\text{J}}{\text{K}}.$$

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