You are boiling pasta and absentmindedly grab a copper stirring spoon rather than your wooden spoon. The copper spoon has a 20 mm ×1.5 mm rectangular cross section, and the distance from the boiling water to your 35°C hand is 18 cm. How long does it take the spoon to transfer 25 J of energy to your hand?
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Heat Transfer
Problem 73a
Textbook Question
A house has a volume of 1200 m³. What is the total mass of air inside the house at 15°C?
Verified step by step guidance1
Determine the density of air at 15°C. The density of air can be approximated using the ideal gas law or obtained from standard tables. At 15°C, the density of air is approximately 1.225 kg/m³.
Use the formula for mass: \( m = \rho \cdot V \), where \( m \) is the mass, \( \rho \) is the density of air, and \( V \) is the volume of the house.
Substitute the given values into the formula: \( \rho = 1.225 \; \text{kg/m}^3 \) and \( V = 1200 \; \text{m}^3 \).
Perform the multiplication: \( m = 1.225 \cdot 1200 \).
The result will give you the total mass of air inside the house in kilograms.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Density of Air
Density is defined as mass per unit volume and is a crucial property of substances, including air. At standard conditions, the density of air at 15°C is approximately 1.225 kg/m³. This value can vary with temperature and pressure, but it provides a baseline for calculating the mass of air in a given volume.
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Intro to Density
Ideal Gas Law
The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law helps in understanding how gases behave under different conditions, which is essential for calculating the mass of air in the house.
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Ideal Gases and the Ideal Gas Law
Mass Calculation
To find the total mass of air in the house, the formula used is mass = density × volume. By multiplying the density of air at 15°C by the volume of the house (1200 m³), one can determine the total mass of air present. This straightforward calculation is fundamental in various physics and engineering applications.
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