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Chapter 15: Problem 48

An ice cube at \(0.0^{\circ} \mathrm{C}\) is slowly melting. What is the change in the ice cube's entropy for each \(1.00 \mathrm{g}\) of ice that melts?

Short Answer

Expert verified
Answer: The change in entropy for every 1.00 g of ice that melts from 0.0°C is approximately 1.22 J/K.

Step by step solution

01

Determine the heat of fusion of ice

The heat of fusion is the amount of heat required to change a substance from the solid phase to the liquid phase without changing its temperature. For ice, the heat of fusion is equal to \(333.55 \mathrm{J/g}\).
02

Calculate the heat needed for melting 1 gram of ice

For every \(1.00 \mathrm{g}\) of ice that melts, we can determine the total heat needed for the process by multiplying the heat of fusion by the mass of ice. $$Q = m \times L = (1.00 \thinspace \mathrm{g}) \times (333.55 \thinspace \mathrm{J/g}) = 333.55 \thinspace \mathrm{J}$$
03

Calculate the change in entropy

To calculate the change in entropy, we will use the formula: $$\Delta S = \frac{Q}{T}$$ where \(\Delta S\) is the change in entropy, \(Q\) is the heat added to the system, and \(T\) is the temperature. Remember to use temperature in Kelvin. First, convert the temperature to Kelvin: $$T_{\text{K}} = T_{\text{C}} + 273.15 = 0.0^{\circ} \mathrm{C} + 273.15 \thinspace\mathrm{K} = 273.15 \thinspace\mathrm{K}$$ Now, calculate the change in entropy: $$\Delta S = \frac{333.55 \thinspace \mathrm{J}}{273.15 \thinspace \mathrm{K}} \approx 1.22 \thinspace \mathrm{J/K}$$ So, for every \(1.00 \mathrm{g}\) of ice that melts, the change in the ice cube's entropy is approximately \(1.22 \thinspace \mathrm{J/K}\).

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Most popular questions from this chapter

A reversible refrigerator has a coefficient of performance of \(3.0 .\) How much work must be done to freeze \(1.0 \mathrm{kg}\) of liquid water initially at \(0^{\circ} \mathrm{C} ?\)
A monatomic ideal gas at \(27^{\circ} \mathrm{C}\) undergoes a constant volume process from \(A\) to \(B\) and a constant pressure process from \(B\) to \(C\) Find the total work done during these two processes.
An air conditioner whose coefficient of performance is 2.00 removes $1.73 \times 10^{8} \mathrm{J}$ of heat from a room per day. How much does it cost to run the air conditioning unit per day if electricity costs \(\$ 0.10\) per kilowatt-hour? (Note that 1 kilowatt-hour \(=3.6 \times 10^{6} \mathrm{J} .\) )
A reversible engine with an efficiency of \(30.0 \%\) has $T_{\mathrm{C}}=310.0 \mathrm{K} .\( (a) What is \)T_{\mathrm{H}} ?$ (b) How much heat is exhausted for every \(0.100 \mathrm{kJ}\) of work done?
A \(0.500-\mathrm{kg}\) block of iron at \(60.0^{\circ} \mathrm{C}\) is placed in contact with a \(0.500-\mathrm{kg}\) block of iron at $20.0^{\circ} \mathrm{C} .\( (a) The blocks soon come to a common temperature of \)40.0^{\circ} \mathrm{C} .$ Estimate the entropy change of the universe when this occurs. [Hint: Assume that all the heat flow occurs at an average temperature for each block.] (b) Estimate the entropy change of the universe if, instead, the temperature of the hotter block increased to \(80.0^{\circ} \mathrm{C}\) while the temperature of the colder block decreased to \(0.0^{\circ} \mathrm{C}\) [Hint: The answer is negative, indicating that the process is impossible. \(]\)
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