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(a) What is the entropy change of 1.00 mol of \(\mathrm{H}_{2} \mathrm{O}\) when it changes from ice to water at \(0.0^{\circ} \mathrm{C} ?\) (b) If the ice is in contact with an environment at a temperature of \(10.0^{\circ} \mathrm{C}\) what is the entropy change of the universe when the ice melts?

Short Answer

Expert verified
Answer: The entropy change of the universe when the ice melts is 0.8 J/K.

Step by step solution

01

(a) Calculate the entropy change of the system

First, we need to find the heat transferred during the phase change. The heat of fusion (q) for water is 6.01 kJ/mol. Since we have 1 mol of ice, we can compute the heat transfer as follows: q = (1.00 mol) × (6.01 kJ/mol) = 6.01 kJ Now, we should convert the temperature from Celsius to Kelvin: T(K) = T(°C) + 273.15 = 0.0 + 273.15 = 273.15 K Next, we can calculate the entropy change (ΔS) using the formula ΔS = q/T: ΔS_system = (6.01 kJ) / (273.15 K) = 0.0220 kJ/K = 22.0 J/K (rounded to 2 decimal places)
02

(b) Calculate the entropy change of the universe

In this part, we have to find the entropy change of the environment when the ice melts. The heat transfer to the environment is the same as the heat absorbed by the ice: q_environment = -6.01 kJ (negative because heat is released to the environment) Since the temperature of the environment is 10.0°C, we should first convert it to Kelvin: T_environment(K) = T_environment(°C) + 273.15 = 10.0 + 273.15 = 283.15 K Now we can calculate the entropy change (ΔS) for the environment: ΔS_environment = (q_environment) / (T_environment) = (-6.01 kJ) / (283.15 K) = -0.0212 kJ/K = -21.2 J/K (rounded to 2 decimal places) Finally, we'll find the total entropy change of the universe, which is the sum of the entropy changes for the system and the environment: ΔS_universe = ΔS_system + ΔS_environment = 22.0 J/K + (-21.2 J/K) = 0.8 J/K (rounded to 2 decimal places) The entropy change of the universe when the ice melts is 0.8 J/K.

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Most popular questions from this chapter

A large block of copper initially at \(20.0^{\circ} \mathrm{C}\) is placed in a vat of hot water \(\left(80.0^{\circ} \mathrm{C}\right) .\) For the first $1.0 \mathrm{J}$ of heat that flows from the water into the block, find (a) the entropy change of the block, (b) the entropy change of the water, and (c) the entropy change of the universe. Note that the temperatures of the block and water are essentially unchanged by the flow of only \(1.0 \mathrm{J}\) of heat.
A coal-fired electrical generating station can use a higher \(T_{\mathrm{H}}\) than a nuclear plant; for safety reasons the core of a nuclear reactor is not allowed to get as hot as coal. Suppose that $T_{\mathrm{H}}=727^{\circ} \mathrm{C}\( for a coal station but \)T_{\mathrm{H}}=527^{\circ} \mathrm{C}$ for a nuclear station. Both power plants exhaust waste heat into a lake at \(T_{\mathrm{C}}=27^{\circ} \mathrm{C} .\) How much waste heat does each plant exhaust into the lake to produce \(1.00 \mathrm{MJ}\) of electricity? Assume both operate as reversible engines.
An ideal engine has an efficiency of 0.725 and uses gas from a hot reservoir at a temperature of \(622 \mathrm{K}\). What is the temperature of the cold reservoir to which it exhausts heat?

Show that the coefficient of performance for a reversible refrigerator is \(1 /\left[\left(T_{\mathrm{H}} / T_{\mathrm{C}}\right)-1\right]\).

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