Math

QuestionCalculate the specific heat capacity of a plece of wood if 1500.0 g of the wood absorbs 67,500 joules of heat, and its temperature changes from 32C32^{\circ} \mathrm{C} to 57C57^{\circ} \mathrm{C}.

Studdy Solution

STEP 1

1. The mass of the wood is 1500.0 1500.0 grams.
2. The heat absorbed by the wood is 67,500 67,500 joules.
3. The initial temperature of the wood is 32C 32^{\circ} \mathrm{C} .
4. The final temperature of the wood is 57C 57^{\circ} \mathrm{C} .

STEP 2

1. Recall the formula for specific heat capacity.
2. Calculate the change in temperature.
3. Substitute the given values into the formula.
4. Solve for the specific heat capacity.

STEP 3

Recall the formula for specific heat capacity:
q=mcΔT q = mc\Delta T
where q q is the heat absorbed, m m is the mass, c c is the specific heat capacity, and ΔT\Delta T is the change in temperature.

STEP 4

Calculate the change in temperature:
ΔT=TfinalTinitial \Delta T = T_{\text{final}} - T_{\text{initial}} =57C32C = 57^{\circ} \mathrm{C} - 32^{\circ} \mathrm{C} =25C = 25^{\circ} \mathrm{C}

STEP 5

Substitute the given values into the formula:
67,500J=1500.0g×c×25C 67,500 \, \text{J} = 1500.0 \, \text{g} \times c \times 25^{\circ} \mathrm{C}

STEP 6

Solve for the specific heat capacity c c :
c=67,500J1500.0g×25C c = \frac{67,500 \, \text{J}}{1500.0 \, \text{g} \times 25^{\circ} \mathrm{C}} =67,50037,500 = \frac{67,500}{37,500} =1.8J/gC = 1.8 \, \text{J/g}^{\circ}\mathrm{C}
The specific heat capacity of the wood is:
1.8J/gC \boxed{1.8 \, \text{J/g}^{\circ}\mathrm{C}}

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