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 85

Chapter 19, Problem 85

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).

Verified step by step guidance

Step 1: Calculate the energy required to heat the water from 20°C to 100°C using the formula for heat transfer: Q = mcΔT, where m is the mass of the water (250 g = 0.250 kg), c is the specific heat capacity of water (approximately 4186 J/kg·°C), and ΔT is the temperature change (100°C - 20°C = 80°C).

Step 2: Determine the rate at which the oven puts energy into the water by dividing the total energy (Q) by the time (t = 105 s). Use the formula: Power = Q / t.

Step 3: For part (b), calculate the energy delivered by the oven in 2 minutes (120 s) using the power calculated in Step 2. Use the formula: Energy = Power × time.

Step 4: Determine the energy required to boil away a certain mass of water using the formula: Q = mL, where m is the mass of water to be boiled away and L is the latent heat of vaporization of water (approximately 2260 kJ/kg).

Step 5: Solve for the mass of water that boils away by dividing the energy delivered during the additional time (from Step 3) by the latent heat of vaporization (L).

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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 energy required to raise the temperature of a unit mass of a substance by one degree Celsius. For water, this value is approximately 4.18 J/g°C. Understanding this concept is crucial for calculating the energy needed to heat water, as it directly relates the mass of the water, the temperature change, and the energy input.

Power and Energy Transfer

Power is defined as the rate at which energy is transferred or converted. It is measured in watts (W), where 1 W equals 1 joule per second. In the context of the microwave oven, knowing the power output allows us to determine how much energy is supplied to the water over a given time, which is essential for solving the first part of the question.

Phase Change and Latent Heat

When a substance changes from one phase to another, such as from liquid to gas, it requires energy known as latent heat. For water, the latent heat of vaporization is the energy needed to convert water at its boiling point into steam without changing its temperature. This concept is vital for calculating how much water will boil away when the microwave operates for an extended period.

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Related Practice

Textbook Question

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.

Textbook Question

(a) Estimate the total power radiated into space by the Sun, assuming it to be a perfect emitter at T = 5500 K. The Sun’s radius is 7.0 x 10⁸ m.

(b) From this, determine the power per unit area arriving at the Earth, 1.5 x 10¹¹ m away (Fig. 19–37).

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Textbook Question

What will be the final result when equal masses of ice at 0°C and steam at 100°C are mixed together?

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Textbook Question

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

Textbook Question

A copper rod and an aluminum rod of the same length and cross-sectional area are attached end to end (Fig. 19–35). The copper end is placed in a furnace maintained at a constant temperature of 205°C. The aluminum end is placed in an ice bath held at a constant temperature of 0.0°C. Calculate the temperature at the point where the two rods are joined.

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