Textbook Question
A sophomore with nothing better to do adds heat to kg of ice at °C until it is all melted. What is the change in entropy of the water?
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Ch 20: The Second Law of Thermodynamics
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 20, Problem 24a
You make tea with kg of °C water and let it cool to room temperature (°C). Calculate the entropy change of the water while it cools.
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Identify the initial and final temperatures of the water. The initial temperature \( T_i \) is 85.0°C, and the final temperature \( T_f \) is room temperature, which is typically around 20.0°C. Convert these temperatures to Kelvin by adding 273.15 to each.
Use the formula for the change in entropy \( \Delta S \) for a substance with constant specific heat capacity: \( \Delta S = m \cdot c \cdot \ln\left(\frac{T_f}{T_i}\right) \), where \( m \) is the mass of the water, \( c \) is the specific heat capacity of water (approximately 4.18 J/g°C), and \( T_f \) and \( T_i \) are the final and initial temperatures in Kelvin.
Substitute the mass of the water \( m = 0.250 \) kg (or 250 g), the specific heat capacity \( c = 4.18 \) J/g°C, and the converted temperatures into the entropy change formula.
Calculate the natural logarithm \( \ln\left(\frac{T_f}{T_i}\right) \) using the temperatures in Kelvin.
Multiply the mass, specific heat capacity, and the natural logarithm result to find the change in entropy \( \Delta S \). Ensure the units are consistent throughout the calculation.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Entropy
Entropy is a measure of the disorder or randomness in a system, often associated with the second law of thermodynamics. It quantifies the amount of energy in a system that is unavailable for doing work. In thermodynamic processes, entropy tends to increase, indicating a move towards equilibrium and maximum disorder.
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Specific Heat Capacity
Specific heat capacity is the amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius. It is a property that varies with the material and is crucial for calculating the heat exchange in processes involving temperature changes, such as cooling or heating.
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Temperature Change
Temperature change refers to the difference in temperature between the initial and final states of a substance. It is a key factor in calculating the entropy change, as it affects the heat transfer and the energy distribution within the system. Understanding how temperature affects entropy is essential for thermodynamic calculations.
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Related Practice
Textbook Question
You decide to take a nice hot bath but discover that your thoughtless roommate has used up most of the hot water. You fill the tub with kg of °C water and attempt to warm it further by pouring in kg of boiling water from the stove. Is this a reversible or an irreversible process? Use physical reasoning to explain.
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Textbook Question
A lonely party balloon with a volume of L and containing mol of air is left behind to drift in the temporarily uninhabited and depressurized International Space Station. Sunlight coming through a porthole heats and explodes the balloon, causing the air in it to undergo a free expansion into the empty station, whose total volume is m3. Calculate the entropy change of the air during the expansion.
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Textbook Question
Two moles of an ideal gas occupy a volume . The gas expands isothermally and reversibly to a volume . Is the velocity distribution changed by the isothermal expansion? Explain.
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Textbook Question
A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. In minutes of operation, the heat rejected by the engine melts kg of ice. During this time, how much work is performed by the engine?
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