Lead has a density of 1.13 104 kg/m3 at 0°C.
(a) What is the density of lead at 86°C?
___kg/m3
(b) Based on your answer to part (a), now consider a situation in which you plan to invest in a gold bar. Would you be better off buying it on a warm day?
Yes or No
Explain.
To find the density of lead at 86°C, we can use the information provided. The density of lead at 0°C is given as 1.13 x 10^4 kg/m^3.
(a) The density of a substance typically changes with temperature. To find the density of lead at 86°C, we need to account for this change. In general, the density of most substances decreases with increasing temperature.
To calculate the density of lead at 86°C, we can use the following formula:
Density at T2 = Density at T1 * (1 + Beta * (T2 - T1))
where T2 is the final temperature (86°C), T1 is the initial temperature (0°C), and Beta is the thermal expansion coefficient.
The thermal expansion coefficient for lead is approximately 0.0000291 per °C.
Now, let's substitute the values into the formula:
Density at 86°C = 1.13 x 10^4 kg/m^3 * (1 + 0.0000291 per °C * (86°C - 0°C))
Calculating the expression inside the parentheses:
Density at 86°C = 1.13 x 10^4 kg/m^3 * (1 + 0.0000291 per °C * 86°C)
Density at 86°C = 1.13 x 10^4 kg/m^3 * (1 + 0.0000291 * 86)
Density at 86°C ≈ 1.13 x 10^4 kg/m^3 * (1 + 0.0025066)
Density at 86°C ≈ 1.13 x 10^4 kg/m^3 * 1.0025066
Density at 86°C ≈ 1.13000418 x 10^4 kg/m^3
Therefore, the density of lead at 86°C is approximately 1.13000418 x 10^4 kg/m^3.
(b) Now, let's consider the situation of investing in a gold bar. We need to decide whether it would be better to buy the gold bar on a warm day, considering the change in density with temperature.
Since the density of most substances decreases with increasing temperature, we can conclude that the density of gold would also decrease with increasing temperature.
If you plan to invest in a gold bar, buying it on a warm day may not be favorable. When the temperature rises, the density of gold decreases. Therefore, you would be paying the same amount of money for a gold bar that has a slightly lower density at a higher temperature. This means that you would be getting slightly less gold for the same price.
In conclusion, it is generally better to buy a gold bar on a cooler day, as the density would be higher, ensuring that you are getting the maximum value for your investment.