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Chapter 2: Problem 50

Suppose you have a 2.000-pound block of iron at \(50.0^{\circ} \mathrm{C}\). How much heat in joules would it take to warm this block to \(75.0^{\circ} \mathrm{C}\) ?

Short Answer

Expert verified
The heat required to warm the iron block to \(75.0^{\circ}\mathrm{C}\) is approximately \(1.0 \times 10^4 \mathrm{J}\).

Step by step solution

01

Determine mass of the iron block (in kilograms)

Given the mass of the iron block is 2.000 pounds, we need to convert it into kilograms (kg) for our calculation since we'll be using SI units. The conversion factor is 1 pound = 0.453592 kg. Mass in kg = Mass in pounds × Conversion factor Mass in kg = 2.000 pounds × 0.453592 kg/pound Mass in kg = 0.907185 kg
02

Find the specific heat capacity of iron

The specific heat capacity of a substance is the amount of heat needed to raise the temperature of 1 kg of the substance by 1°C. To determine the heat required to warm the iron block, we need to know the specific heat capacity of iron. The specific heat capacity of iron is 449 J/kg·°C.
03

Calculate the temperature change

The initial temperature of the iron block is given as 50.0°C, and it needs to be heated to reach a final temperature of 75.0°C. We can find the temperature change by subtracting the initial temperature from the final temperature. ΔT = T_final - T_initial ΔT = 75.0°C - 50.0°C ΔT = 25.0°C
04

Use the formula to calculate heat required

Now that we have all the necessary values, we can use the formula for calculating heat absorbed or released during a change in temperature: Q = mcΔT Where Q represents the heat in joules, m is the mass of the iron block, c is the specific heat capacity of iron, and ΔT is the temperature change. Q = (0.907185 kg) × (449 J/kg·°C) × (25.0°C) Q = 10197.798 J
05

Round the answer to two significant figures

Since the least number of significant digits is 2 (the given mass is 2.000), we round the answer to two significant digits. The heat required to warm the iron block to 75.0°C is: Q = 1.0 × 10^4 J

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Most popular questions from this chapter

Without doing any numerical calculations, determine which would have the smallest volume: (a) \(50 \mathrm{~g}\) of water (density \(=1.0 \mathrm{~g} / \mathrm{mL}\) ) (b) \(50 \mathrm{~g}\) of salt water (density \(=2.3 \mathrm{~g} / \mathrm{mL}\) ) (c) \(50 \mathrm{~g}\) of mercury (density \(=13.6 \mathrm{~g} / \mathrm{mL}\) ) (d) \(50 \mathrm{~g}\) of alcohol (density \(=0.89 \mathrm{~g} / \mathrm{mL}\) ) Explain your reasoning.

Indicate the number of significant figures in: (a) \(0.503200 \mathrm{~mL}\) (b) \(2000 \pm 5\) (c) \(2000 \pm 50\) (d) \(2000 \pm 0.5\) (e) \(200.1\)

Express each mass in grams, both in standard notation and in scientific notation: (a) \(536 \mathrm{mg}\) (b) \(8.26 \mathrm{dg}\) (c) \(0.0057 \mu \mathrm{g}\) (d) \(139 \mathrm{~kg}\) (e) \(836 \mathrm{ng}\) (f) \(0.073 \mathrm{Mg}\)

Write each number in standard notation: (a) \(1.79 \times 10^{-2}\) (b) \(8.76 \times 10^{-9}\) (c) \(4.88 \times 10^{10}\) (d) \(7.52 \times 10^{1}\) (e) \(8.37 \times 10^{\circ}\) (f) \(4.184 \times 10^{4}\)

A physician has ordered \(325 \mathrm{mg}\) of atropine to be given to a patient intramuscularly. If atropine were available as a solution that contained \(5000 \mu\) \(\mathrm{g} / \mathrm{mL}\), how many milliliters would you need to give the patient?
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