Determine the energy to heat a cube of gold with a volume of 19.0{\rm cm}^{3} from 15^\circ C to 37^\circ C. (Figure 1)
Refer to the tables of densities (Figure 2) and to the table of the specific heats (Figure 3)
To determine the energy required to heat the cube of gold, we need to follow these steps:
1. Determine the mass of the gold cube.
2. Calculate the change in temperature.
3. Use the specific heat of gold to calculate the energy.
Let's start with step 1:
1. To find the mass of the gold cube, we need to use its volume and density. Refer to "Figure 2" for the densities table.
The density of gold is given as 19.3 g/cm^3. Therefore, we can calculate the mass using the formula:
mass = density x volume
Substituting the given values, we have:
mass = 19.3 g/cm^3 x 19.0 cm^3
mass = 366.7 g
So, the mass of the gold cube is 366.7 grams.
Now, let's move on to step 2:
2. Calculate the change in temperature. The change in temperature is given as 37°C - 15°C = 22°C.
Finally, let's proceed to step 3:
3. Use the specific heat of gold to calculate the energy. Refer to "Figure 3" for the specific heat table.
The specific heat capacity of gold is 0.129 J/g·°C. Therefore, we can calculate the energy using the formula:
energy = mass x specific heat x change in temperature
Substituting the given values, we have:
energy = 366.7 g x 0.129 J/g·°C x 22°C
energy ≈ 1010.56 J
Therefore, the energy required to heat the cube of gold from 15°C to 37°C is approximately 1010.56 J.