A block of aluminum with a volume of 98.5 cm3 absorbs 67.4 J of heat. If its initial temperature was 32.5°C, what is its final temperature? (density of aluminum = 2.70g/cm3)
Use density to convert volume Al to mass. m = volume x density.
J = mass Al x sp.h. Al x (Tfinal-Tinitial). Subsitute and solve for Tf.
32.8
To find the final temperature of the aluminum block, we can use the concept of specific heat and the equation:
Q = m * c * ΔT
where:
Q = heat absorbed by the aluminum block (in Joules)
m = mass of the aluminum block (in kg)
c = specific heat capacity of aluminum (in J/g°C)
ΔT = change in temperature (in °C)
First, let's find the mass of the aluminum block using its volume and density:
Density = Mass / Volume
Rearranging the equation, we can solve for mass:
Mass = Density * Volume
Mass = 2.70 g/cm^3 * 98.5 cm^3
Now, let's convert the mass to kilograms:
Mass = (2.70 g/cm^3 * 98.5 cm^3) / 1000 g/kg = 0.261 kg
Next, let's rearrange the specific heat equation to solve for the change in temperature:
ΔT = Q / (m * c)
We have the values for Q, m, and c:
Q = 67.4 J
m = 0.261 kg
c = specific heat capacity of aluminum (which we can look up)
Now, we need to find the specific heat capacity of aluminum. The specific heat capacity of aluminum is typically around 0.90 J/g°C.
Now, substitute the values into the equation:
ΔT = 67.4 J / (0.261 kg * 0.90 J/g°C)
Calculating the value:
ΔT ≈ 265.85 °C
To find the final temperature, we add the change in temperature to the initial temperature:
Final Temperature = Initial Temperature + ΔT
Final Temperature = 32.5°C + 265.85°C
Calculating the value:
Final Temperature ≈ 298.35°C
Therefore, the final temperature of the aluminum block is approximately 298.35°C.
To find the final temperature of the aluminum block, we need to use the formula:
Q = mcΔT
Where:
Q = heat absorbed (in joules)
m = mass of the aluminum block (in grams)
c = specific heat capacity of aluminum (in J/g°C)
ΔT = change in temperature (in °C)
To calculate the mass of the aluminum block, we can use its density:
density = mass/volume
Given that the density of aluminum is 2.70 g/cm3 and the volume of the block is 98.5 cm3, we can calculate the mass:
mass = density * volume
mass = 2.70 g/cm3 * 98.5 cm3
Now let's calculate the mass.
mass = 265.95 grams
Next, we need to calculate the change in temperature (ΔT). We are given that the initial temperature is 32.5°C, but we do not have the final temperature. Therefore, we introduce a variable for the final temperature, which we will solve for.
Now we can rearrange the formula to solve for the final temperature:
ΔT = (Q) / (mc)
Final temperature = (Q / (mc)) + initial temperature
Substituting the known values:
Final temperature = (67.4 J) / ((265.95 g) * (0.90 J/g°C)) + 32.5°C
Now we can calculate the final temperature.