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QuestionHow much energy is needed to heat 10 g10 \mathrm{~g} of iron vs. aluminum by 1∘C1{ }^{\circ} \mathrm{C}?
CFe=0.450Jg⋅∘CCAl=0.900Jg⋅∘C \mathrm{C}_{\mathrm{Fe}}=0.450 \frac{\mathrm{J}}{\mathrm{g} \cdot{ }^{\circ} \mathrm{C}} \quad \mathrm{C}_{\mathrm{Al}}=0.900 \frac{\mathrm{J}}{\mathrm{g} \cdot{ }^{\circ} \mathrm{C}}
A. Fe needs twice as much energy as Al B. Fe needs half as much energy as Al C. Fe needs 0.450 times less energy than Al D. Fe needs 0.450 times more energy than Al

Studdy Solution

STEP 1

Assumptions1. The mass of iron (Fe) is10g. The mass of aluminum (Al) is10g3. The specific heat capacity of iron (C_Fe) is0.450 J/g°C4. The specific heat capacity of aluminum (C_Al) is0.900 J/g°C5. The temperature change for both substances is1°C

STEP 2

The energy required to change the temperature of a substance can be calculated using the formulaEnergy=masstimesspecific heat capacitytimeschange in temperatureEnergy = mass \\times specific\, heat\, capacity \\times change\, in\, temperature

STEP 3

First, let's calculate the energy required to raise the temperature of the iron by1°C.
EnergyFe=massFetimesCFetimesΔFeEnergy_{Fe} = mass_{Fe} \\times C_{Fe} \\times \Delta_{Fe}

STEP 4

Plug in the values for the mass of iron, the specific heat capacity of iron, and the temperature change to calculate the energy.
EnergyFe=10gtimes0.450Jg°Ctimes1°CEnergy_{Fe} =10g \\times0.450 \frac{J}{g°C} \\times1°C

STEP 5

Calculate the energy required to raise the temperature of the iron by1°C.
EnergyFe=10gtimes0.450Jg°Ctimes1°C=4.5JEnergy_{Fe} =10g \\times0.450 \frac{J}{g°C} \\times1°C =4.5J

STEP 6

Now, let's calculate the energy required to raise the temperature of the aluminum by1°C.
EnergyAl=massAltimesCAltimesΔAlEnergy_{Al} = mass_{Al} \\times C_{Al} \\times \Delta_{Al}

STEP 7

Plug in the values for the mass of aluminum, the specific heat capacity of aluminum, and the temperature change to calculate the energy.
EnergyAl=10gtimes0.900Jg°Ctimes1°CEnergy_{Al} =10g \\times0.900 \frac{J}{g°C} \\times1°C

STEP 8

Calculate the energy required to raise the temperature of the aluminum by1°C.
EnergyAl=10gtimes0.900Jg°Ctimes1°C=JEnergy_{Al} =10g \\times0.900 \frac{J}{g°C} \\times1°C =J

STEP 9

Now that we have the energy required to raise the temperature of both substances by°C, we can compare these values to find the answer.
EnergyFeEnergyAl=4.5J9J=.5\frac{Energy_{Fe}}{Energy_{Al}} = \frac{4.5J}{9J} =.5This means that iron needs half as much energy as aluminum to raise the temperature by°C. So, the correct answer is B. Fe needs half as much energy as Al.

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