At 25 degrees celsius, the dimensions of a rectangular block of gold are 4.42 cm by 3.07 cm by 2.63 cm. The mass of the gold is 689g.
I found that the density is 19.3g/cm^3 at 25 degrees
but how will the density change if the temperature is increased to 125 degrees?
To determine how the density of gold will change when the temperature is increased from 25 degrees Celsius to 125 degrees Celsius, we need to consider the effect of temperature on the density of the substance.
The density of a substance tends to change with temperature due to thermal expansion. When the temperature increases, most substances expand and therefore occupy a larger volume, resulting in a decrease in density. However, this behavior may not be uniform across all materials.
To calculate the new density at 125 degrees Celsius, we can use the coefficient of thermal expansion for gold. The coefficient of thermal expansion (α) represents how much a material expands or contracts per unit change in temperature.
For gold, the coefficient of thermal expansion (α) is approximately 14.2 x 10^-6 °C^-1.
Here's how to calculate the new density:
1. Calculate the change in temperature:
ΔT = T₂ - T₁
ΔT = 125°C - 25°C
ΔT = 100°C
2. Use the formula for linear expansion to calculate the change in length:
ΔL = α * L * ΔT
α = coefficient of thermal expansion for gold
L = original length
Assuming the change in length is negligible compared to the dimensions of the gold block, we can directly use the coefficient of thermal expansion to calculate the change in volume.
3. Calculate the change in volume:
ΔV = α * V * ΔT
α = coefficient of thermal expansion for gold
V = original volume
4. Calculate the new volume:
V_new = V + ΔV
5. Calculate the new density:
density_new = mass / V_new
By following these steps, you can determine the new density of the gold at 125 degrees Celsius.