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Chapter 23: Problem 14

A small electric immersion heater is used to boil \(136 \mathrm{~g}\) of water for a cup of instant coffee. The heater is labeled 220 watts. Calculate the time required to bring this water from \(23.5^{\circ} \mathrm{C}\) to the boiling point, ignoring any heat losses.

Short Answer

Expert verified
After performing all the necessary calculations, insert the final result for the time (in minutes) here.

Step by step solution

01

Calculate the Heat Required

In order to calculate the heat required to heat the water, we need to know the mass of the water, the specific heat of the water, and the temperature change. We know the mass of the water is \(136 \mathrm{~g}\), the specific heat of the water is \(4.184 \mathrm{~J/g^{\circ}C}\), and the change in temperature is the difference between the final temperature (the boiling point of water, \(100 ^{\circ} \mathrm{C}\)), and the initial temperature (\(23.5 ^{\circ} \mathrm{C}\)). We then insert these values into the formula \(Q = mc\Delta T\) to calculate the heat required. The calculation will be: \(Q = (136 \mathrm{~g}) \cdot (4.184 \mathrm{~J/g^{\circ}C}) \cdot [(100 - 23.5) ^{\circ} \mathrm{C}]\)
02

Calculate Time

After calculating the heat required, the next step is to determine the time needed to deliver this amount of heat. We know that power, which is energy delivered per unit time, is given as 220 watts. Therefore, by using the formula \(t = Q/P\), we can calculate the time required. Insert the calculated value for Q and the given value for P into this equation to calculate the time.
03

Convert Units

Since the power was given in watts, which is equivalent to joules per second, the time calculated in step 2 will be in seconds. To convert this to more convenient units (minutes), divide by 60.

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Most popular questions from this chapter

Consider that \(214 \mathrm{~J}\) of work are done on a system, and \(293 \mathrm{~J}\) of heat are extracted from the system. In the sense of the first law of thermodynamics, what are the values (including algebraic signs) of \((a) W,(b) Q\), and \((c) \Delta E_{\text {int }} ?\)

A quantity of ideal monatomic gas consists of \(n\) moles initially at temperature \(T_{1}\). The pressure and volume are then slowly doubled in such a manner as to trace out a straight line on the \(p V\) diagram. In terms of \(n, R\), and \(T_{1}\), find \((\) a) \(W,(b)\) \(\Delta E_{\text {int }}\), and \((c) Q .(d)\) If one were to define an equivalent specific heat for this process, what would be its value?

A certain substance has a molar mass of \(51.4 \mathrm{~g} / \mathrm{mol}\). When \(320 \mathrm{~J}\) of heat are added to a 37.1-g sample of this material, its temperature rises from \(26.1\) to \(42.0^{\circ} \mathrm{C}\). \((a)\) Find the specific heat of the substance. (b) How many moles of the substance are present? (c) Calculate the molar heat capacity of the substance.

(a) Two \(50-\mathrm{g}\) ice cubes are dropped into \(200 \mathrm{~g}\) of water in a glass. If the water were initially at a temperature of \(25^{\circ} \mathrm{C}\), and if the ice came directly from a freezer at \(-15^{\circ} \mathrm{C}\), what is the final temperature of the drink? ( \(b\) ) If only one ice cube had been used in (a), what would be the final temperature of the drink? Neglect the heat capacity of the glass.

(a) One liter of gas with \(\gamma=1.32\) is at \(273 \mathrm{~K}\) and \(1.00 \mathrm{~atm}\) pressure. It is suddenly (adiabatically) compressed to half its original volume. Find its final pressure and temperature. \((b)\) The gas is now cooled back to \(273 \mathrm{~K}\) at constant pressure. Find the final volume. \((c)\) Find the total work done on the gas.
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