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Chapter 5: Problem 50

Two solid objects, \(A\) and \(B\), are placed in boiling water and allowed to come to temperature there. Each is then lifted out and placed in separate beakers containing \(1000 \mathrm{~g}\) water at \(10.0^{\circ} \mathrm{C}\). Object A increases the water temperature by \(3.50^{\circ} \mathrm{C}\); B increases the water temperature by \(2.60^{\circ} \mathrm{C}\). (a) Which object has the larger heat capacity? (b) What can you say about the specific heats of \(\mathrm{A}\) and \(\mathrm{B}\) ?

Short Answer

Expert verified
The object A has a larger heat capacity as it transfers more heat (\(14630 \mathrm{~J}\)) to the water in the beaker compared to object B (\(10868 \mathrm{~J}\)). We can't determine the specific heats of A and B without more information, but since A has a larger heat capacity, its specific heat is likely to be higher than the specific heat of B.

Step by step solution

01

Define heat capacity and specific heat

Heat capacity is the amount of heat required to change the temperature of an object by 1 degree Celsius (or other temperature unit). Specific heat is the heat capacity per unit mass, i.e., the amount of heat required to change the temperature of 1 gram of an object by 1 degree Celsius.
02

Calculate the heat gained by water in each beaker

We are given that object A increased the water temperature by \(3.50^{\circ} \mathrm{C}\) and object B increased the water temperature by \(2.60^{\circ} \mathrm{C}\). The heat gained by the water in each beaker can be calculated using the formula: Heat gained = \(mc\Delta T\) where m is the mass of water (1000 g), c is the specific heat of water \((4.18 \mathrm{~J/g^{\circ}C})\), and ΔT is the change in temperature. Let's calculate the heat gained by the water for both beakers. For object A: Heat gained = \((1000)(4.18)(3.50) = 14630 \mathrm{~J}\) For object B: Heat gained = \((1000)(4.18)(2.60) = 10868 \mathrm{~J}\)
03

Determine the larger heat capacity

Since the two objects were initially at the same temperature (boiling water) and ended up transferring different amounts of heat to the water in the beakers, we can conclude that the object with larger heat capacity absorbed more heat from the boiling water and, therefore, transferred more heat to the water in the beaker. In our case, object A had more heat transferred to the water (\(14630 \mathrm{~J}\)) than object B (\(10868 \mathrm{~J}\)). Hence, object A has the larger heat capacity.
04

Discuss the specific heats of A and B

We can't determine the specific heats of A and B without more information. However, we can make a general statement based on heat capacity differences. Since object A has a larger heat capacity than object B, for the same mass and temperature change, object A will require more heat than object B. Therefore, we can say that the specific heat of A (per unit mass) is likely to be higher than the specific heat of B.

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Most popular questions from this chapter

Consider the decomposition of liquid benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}(l),\) to gaseous acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(g):\) $$ \mathrm{C}_{6} \mathrm{H}_{6}(l) \longrightarrow 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \quad \Delta H=+630 \mathrm{~kJ} $$ (a) What is the enthalpy change for the reverse reaction? (b) What is \(\Delta H\) for the formation of 1 mol of acetylene? (c) Which is more likely to be thermodynamically favored, the forward reaction or the reverse reaction? (d) If \(\mathrm{C}_{6} \mathrm{H}_{6}(g)\) were consumed instead of \(\mathrm{C}_{6} \mathrm{H}_{6}(l),\) would you expect the magnitude of \(\Delta H\) to increase, decrease, or stay the same? Explain.

Diethyl ether, \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}(l),\) a flammable compound that has long been used as a surgical anesthetic, has the structure \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{O}-\mathrm{CH}_{2}-\mathrm{CH}_{3}\) The complete combustion of \(1 \mathrm{~mol}\) of \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}(l)\) to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) yields \(\Delta H^{\circ}=-2723.7 \mathrm{~kJ}\). (a) Write a balanced equation for the combustion of \(1 \mathrm{~mol}\) of \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}(l)\) (b) Write a balanced equation for the formation of \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}(l)\) from its elements. (c) By using the information in this problem and data in Table \(5.3,\) calculate \(\Delta H_{f}^{\circ}\) for diethyl ether.

Methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) is used as a fuel in race cars. (a) Write a balanced equation for the combustion of liquid methanol in air. (b) Calculate the standard enthalpy change for the reaction, assuming \(\mathrm{H}_{2} \mathrm{O}(g)\) as a product. (c) Calculate the heat produced by combustion per liter of methanol. Methanol has a density of \(0.791 \mathrm{~g} / \mathrm{mL}\). (d) Calculate the mass of \(\mathrm{CO}_{2}\) produced per kJ of heat emitted.

The hydrocarbons acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) and benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) have the same empirical formula. Benzene is an "aromatic" hydrocarbon, one that is unusually stable because of its structure. (a) By using data in Appendix \(\mathrm{C}\), determine the standard enthalpy change for the reaction $3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{6}(l)$.

At the end of 2009 , global population was about 6.8 billion people. What mass of glucose in kg would be needed to provide 1500 Cal/person/day of nourishment to the global population for one year? Assume that glucose is metabolized entirely to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) according to the following thermochemical equation: \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)\) \(\Delta H^{\mathrm{o}}=-2803 \mathrm{~kJ}\)
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