Ch. 19 - Heat and the First Law of Thermodynamics

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 19 - Heat and the First Law of Thermodynamics

Problem 99a

Chapter 19, Problem 99a

Calculate what will happen when 1000 J of heat is added to 100 grams of ice at -20°C.

Verified step by step guidance

Step 1: Determine the heat required to raise the temperature of the ice from -20°C to 0°C. Use the formula

Q = m c ΔT

, where

m

is the mass of the ice (100 g = 0.1 kg),

c

is the specific heat capacity of ice (2,100 J/kg·°C), and

ΔT

is the temperature change (20°C).

Step 2: Check if the remaining heat is sufficient to melt the ice. The heat required to melt the ice is calculated using the formula

Q = m L

, where

L

is the latent heat of fusion for ice (334,000 J/kg).

Step 3: If there is still heat remaining after melting the ice, calculate the heat required to raise the temperature of the resulting water from 0°C to a higher temperature. Use the formula

Q = m c ΔT

, where

c

is the specific heat capacity of water (4,186 J/kg·°C).

Step 4: Compare the total heat added (1,000 J) to the sum of the heat required for each step. If the heat is insufficient to complete a step, stop at that point and determine the final state of the system (e.g., partially melted ice or water at a certain temperature).

Step 5: Summarize the final state of the system, specifying whether the ice is fully melted, partially melted, or if the water has reached a certain temperature.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. For ice, this value is approximately 2.09 J/g°C. Understanding this concept is crucial for calculating how much the temperature of ice will increase when heat is added.

Phase Changes

Phase changes refer to the transitions between solid, liquid, and gas states of matter. When heat is added to ice, it may first increase the temperature until it reaches 0°C, and then the heat will be used to convert the ice into water at the melting point. This process requires additional energy known as the latent heat of fusion.

Energy Conservation

The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another. In this context, the heat energy added to the ice will be converted into thermal energy, which will either increase the temperature of the ice or facilitate its phase change into water, depending on the amount of heat supplied.

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The temperature within the Earth’s crust increases about 1.0 C° for each 30 m of depth. The thermal conductivity of the crust is 0.80 J/s C°. Determine the heat transferred from the interior to the surface for the entire Earth in 1.0 h.

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A leaf of area 40cm² and mass 4.5 x 10⁻⁴ kg directly faces the Sun on a clear day. The leaf has an emissivity of 0.85 and a specific heat of 0.80 kcal/kgK. Estimate the energy absorbed per second by the leaf from the Sun.

Textbook Question

A 12-g lead bullet traveling at 220 m/s passes through a thin wall and emerges at a speed of 160 m/s. If the bullet absorbs 50% of the heat generated, If the bullet’s initial temperature was 20°C, will any of the bullet melt, and if so, how much?

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Textbook Question

A microwave oven is used to heat 250 g of water. On its maximum setting, the oven can raise the temperature of the liquid water from 20°C to 100°C in 1 min 45 s ( = 105 s).

(a) At what rate does the oven put energy into the liquid water?

(b) If the power input from the oven to the water remains constant, determine how many grams of water will boil away if the oven is operated for 2 min (rather than just 1 min 45 s).

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Textbook Question

Calculate what will happen when 1000 J of heat is added to 100 grams of water at 100°C.

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