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QuestionRank stainless steel, aluminum, copper, water, and gold by the energy required to heat 10.0 g10.0 \, \text{g} by 25.0∘C25.0^{\circ} \mathrm{C}.

Studdy Solution

STEP 1

Assumptions1. The mass of each substance is 10.0 g10.0 \, \text{g} . The temperature change is 25.0∘C25.0^{\circ} \mathrm{C}
3. The specific heat capacities of the substances are as follows (in J/g°C): stainless steel0.50, aluminum0.897, copper0.385, water4.18, gold0.129

STEP 2

The energy needed to raise the temperature of a substance is given by the formulaQ=mcΔQ = mc\Deltawhere QQ is the energy, mm is the mass, cc is the specific heat capacity, and Δ\Delta is the change in temperature.

STEP 3

We can calculate the energy needed for each substance by plugging in the values into the formula.For stainless steelQsteel=10.0 g×0.50 J/g°C×25.0∘CQ_{\text{steel}} =10.0 \, \text{g} \times0.50 \, \text{J/g°C} \times25.0^{\circ} \mathrm{C}

STEP 4

Calculate the energy for stainless steelQsteel=10.0 g×0.50 J/g°C×25.0∘C=125 JQ_{\text{steel}} =10.0 \, \text{g} \times0.50 \, \text{J/g°C} \times25.0^{\circ} \mathrm{C} =125 \, \text{J}

STEP 5

Repeat the process for aluminumQaluminum=10.0 g×0.897 J/g°C×25.0∘CQ_{\text{aluminum}} =10.0 \, \text{g} \times0.897 \, \text{J/g°C} \times25.0^{\circ} \mathrm{C}

STEP 6

Calculate the energy for aluminumQaluminum=10.0 g×0.897 J/g°C×25.0∘C=224.25 JQ_{\text{aluminum}} =10.0 \, \text{g} \times0.897 \, \text{J/g°C} \times25.0^{\circ} \mathrm{C} =224.25 \, \text{J}

STEP 7

Repeat the process for copperQcopper=10.0 g×0.385 J/g°C×25.0∘CQ_{\text{copper}} =10.0 \, \text{g} \times0.385 \, \text{J/g°C} \times25.0^{\circ} \mathrm{C}

STEP 8

Calculate the energy for copperQcopper=10.0 g×0.385 J/g°C×25.0∘C=96.25 JQ_{\text{copper}} =10.0 \, \text{g} \times0.385 \, \text{J/g°C} \times25.0^{\circ} \mathrm{C} =96.25 \, \text{J}

STEP 9

Repeat the process for waterQwater=. g×4.18 J/g°C×25.∘CQ_{\text{water}} =. \, \text{g} \times4.18 \, \text{J/g°C} \times25.^{\circ} \mathrm{C}

STEP 10

Calculate the energy for waterQwater=10.0 g×4.18 J/g°C×25.0∘C=1045 JQ_{\text{water}} =10.0 \, \text{g} \times4.18 \, \text{J/g°C} \times25.0^{\circ} \mathrm{C} =1045 \, \text{J}

STEP 11

Repeat the process for goldQgold=10.0 g×0.129 J/g°C×25.0∘CQ_{\text{gold}} =10.0 \, \text{g} \times0.129 \, \text{J/g°C} \times25.0^{\circ} \mathrm{C}

STEP 12

Calculate the energy for goldQgold=10.0 g×0.129 J/g°C×25.0∘C=32.25 JQ_{\text{gold}} =10.0 \, \text{g} \times0.129 \, \text{J/g°C} \times25.0^{\circ} \mathrm{C} =32.25 \, \text{J}

STEP 13

Now that we have the energy for each substance, we can rank them from most to least energy needed. The substances are ranked as follows. Water1045 J2. Aluminum224.25 J3. Stainless steel125 J. Copper96.25 J5. Gold32.25 JSo, the substances ranked from most to least energy needed are water, aluminum, stainless steel, copper, gold.

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