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Chapter 7: Problem 113

Several factors are involved in determining the cooking times required for foods in a microwave oven. One of these factors is specific heat. Determine the approximate time required to warm \(250 \mathrm{mL}\) of chicken broth from \(4^{\circ} \mathrm{C}\) (a typical refrigerator temperature) to \(50^{\circ} \mathrm{C}\) in a \(700 \mathrm{W}\) microwave oven. Assume that the density of chicken broth is about \(1 \mathrm{g} / \mathrm{mL}\) and that its specific heat is approximately \(4.2 \mathrm{Jg}^{-1}\) \(^{\circ} \mathrm{C}^{-1}\).

Short Answer

Expert verified
It takes approximately 69 seconds to warm the chicken broth.

Step by step solution

01

Calculate the mass

The first step is to calculate the mass of the chicken broth. The density of the chicken broth is given as \( 1 \, \text{g/mL} \), and the volume is \( 250 \, \text{mL} \). Therefore, the mass \( m \) can be calculated using the formula \( \text{mass} = \text{density} \times \text{volume} \). This results in \( m = 1 \, \text{g/mL} \times 250 \, \text{mL} = 250 \, \text{g} \).
02

Calculate the temperature change

The next step is to calculate the temperature change \( \Delta T \). This is done by subtracting the initial temperature from the final temperature. This results in \( \Delta T = 50^{\circ}C - 4^{\circ}C = 46^{\circ}C \).
03

Calculate the heat required

The heat \( q \) required to warm the chicken broth can now be calculated using the formula \( q = m \cdot c \cdot \Delta T \). The specific heat \( c \) of the chicken broth is given as \( 4.2 \, \text{Jg}^{-1}\text{C}^{-1} \), the mass \( m \) is 250 g, and the temperature change \( \Delta T \) is 46 C. This results in \( q = 250 \, \text{g} \times 4.2 \, \text{Jg}^{-1}\text{C}^{-1} \times 46^{\circ}C = 48300 \, \text{J} \).
04

Calculate the time

The final step is to calculate the time \( t \) it takes to warm the chicken broth. The power \( P \) of the microwave is given as \( 700 \, \text{W} = 700 \, \text{J/s} \). The time can be calculated using the formula \( t = \frac{q}{P} \). This results in \( t = \frac{48300 \, \text{J}}{700 \, \text{J/s}} = 69 \, \text{s} \). Therefore, it takes approximately 69 seconds to warm the chicken broth.

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Most popular questions from this chapter

The standard molar heats of combustion of C(graphite) and \(\mathrm{CO}(\mathrm{g})\) are -393.5 and \(-283 \mathrm{kJ} / \mathrm{mol}\) respectively. Use those data and that for the following reaction $$\mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{COCl}_{2}(\mathrm{g}) \quad \Delta H^{\circ}=-108 \mathrm{kJ}$$ to calculate the standard molar enthalpy of formation of \(\mathrm{COCl}_{2}(\mathrm{g})\).

The following substances undergo complete combustion in a bomb calorimeter. The calorimeter assembly has a heat capacity of \(5.136 \mathrm{kJ} /^{\circ} \mathrm{C} .\) In each case, what is the final temperature if the initial water temperature is \(22.43^{\circ} \mathrm{C} ?\) \(\begin{array}{lllll}\text { (a) } 0.3268 & \text { g caffeine, } & \mathrm{C}_{8} \mathrm{H}_{10} \mathrm{O}_{2} \mathrm{N}_{4} & \text { (heat of }\end{array}\) combustion \(=-1014.2 \mathrm{kcal} / \mathrm{mol} \text { caffeine })\) (b) \(1.35 \mathrm{mL}\) of methyl ethyl ketone, \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}(1)\) \(d=0.805 \mathrm{g} / \mathrm{mL}\) (heat of combustion \(=-2444 \mathrm{kJ} / \mathrm{mol}\) methyl ethyl ketone).

In each of the following processes, is any work done when the reaction is carried out at constant pressure in a vessel open to the atmosphere? If so, is work done by the reacting system or on it? (a) Neutralization of \(\mathrm{Ba}(\mathrm{OH})_{2}(\mathrm{aq})\) by \(\mathrm{HCl}(\mathrm{aq}) ;\) (b) conversion of gaseous nitrogen dioxide to gaseous dinitrogen tetroxide; (c) decomposition of calcium carbonate to calcium oxide and carbon dioxide gas.

What is the change in internal energy of a system if the system (a) absorbs \(58 \mathrm{J}\) of heat and does \(58 \mathrm{J}\) of work; (b) absorbs 125 J of heat and does 687 J of work; (c) evolves 280 cal of heat and has 1.25 kJ of work done on it?

Use Hess's law and the following data $$\begin{aligned} \mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\ \Delta H^{\circ}=-802 \mathrm{kJ} \end{aligned}$$ $$\begin{aligned} \mathrm{CH}_{4}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) & \\ \Delta H^{\circ}=&+247 \mathrm{kJ} \end{aligned}$$ $$\begin{aligned} \mathrm{CH}_{4}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) & \\ \Delta H^{\circ}=&+247 \mathrm{kJ} \end{aligned}$$ $$\begin{aligned} \mathrm{CH}_{4}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) & \\ \Delta H^{\circ}=&+206 \mathrm{kJ} \end{aligned}$$ to determine \(\Delta H^{\circ}\) for the following reaction, an important source of hydrogen gas $$\mathrm{CH}_{4}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g})$$
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