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Chapter 5: Q6E (page 268)

Question: How much heat, in joules and in calories, must be added to a 75.0–g iron block with a specific heat of 0.449 J/g °C to increase its temperature from 25 °C to its melting temperature of 1535 °C?

Short Answer

Expert verified

The heat required to raise the temperature in joules = 50,849 J

The heat required to raise the temperature in calories = 12,147 calories

Step by step solution

01

Step 1: Specific heat

The heat required (Q) to raise the temperature of a substance is given by the formula Q = C × m ×∆ T,where “C” is the specific heat of the substance, “m” is the mass of the substance, and “∆T” is the change in the temperature of the substance.

02

Calculation of heat in Joules

We know from the given details that:

C = 0.449 J/g °C

m = 75 g

T = change in temperature =Tfinal - Tinitial = 15350C – 250C = 15100C

By putting the values above in the equation Q = C × m × ∆ T, we get:

Q = 75 × 0.449 × 1510 = 50,849 J.

The heat required to raise the temperature of 75 g of iron block = 50,849 J

03

Calculation of heat in calories

Also,

1 calorie = 4.184 J.

The heat required to raise the temperature in calories =\(\frac{{50,849}}{{4.186}} = 12147.39cal\)

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Most popular questions from this chapter

Homes may be heated by pumping hot water through radiators. What mass of water will provide the same amount of heat when cooled from 95.0 to 35.0 °C, as the heat provided when 100 g of steam is cooled from 110 °C to 100°C.

Propane, \({{\bf{C}}_{\bf{3}}}{{\bf{H}}_{\bf{8}}}\), is a hydrocarbon that is commonly used as a fuel.

(a) Write a balanced equation for the complete combustion of propane gas.

(b) Calculate the volume of air at 25 °C and 1.00 atmosphere that is needed to completely combust 25.0 grams of propane. Assume that air is 21.0 percent O2 by volume. (Hint: we will see how to do this calculation in a later

chapter on gases—for now use the information that 1.00 L of air at 25 °C and 1.00 atm contains 0.275 g of O2 per liter.)

(c) The heat of combustion of propane is −2,219.2 kJ/mol. Calculate the heat of formation,ΔHf °of propane given thatΔHf °of H2O(l) = −285.8 kJ/mol andΔHf °of CO2(g) = −393.5 kJ/mol.

(d) Assuming that all of the heat released in burning 25.0 grams of propane is transferred to 4.00 kilograms of water, calculate the increase in temperature of the water.

Would the amount of heat measured for the reaction in example 5.5be greater, lesser, or remain the same if we used a calorimeter that was a poorer insulator than a coffee cup calorimeter? Explain your answer.

A piece of unknown metal weighs 217 g. When the metal piece absorbs 1.43 kJ of heat, its temperature increases from 24.5 °C to 39.1 °C. Determine the specific heat of this metal and predict its identity.

One method of generating electricity is by burning coal to heat water, which produces steam that drives an electric generator. To determine the rate at which coal is to be fed into the burner in this type of plant, the heat of combustion per ton of coal must be determined using a bomb calorimeter. When 1.00g of coal is burned in a bomb calorimeter (figure 5.17), the temperature increases by 1.48˚C. If the heat capacity of the calorimeter is 21.6 kJ/˚C, determine the heat produced by the combustion of a ton of coal (2.000 × 103).
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