Question

215 kg of mercury was found to occupy 0.560 ft³ at 20°C. (1) What volume would the mercury occupy at 100 °C? (2) Suppose the mercury is contained in a cylinder having a diameter of 0.25 in. What change in height would be observed as the mercury is heated from 20 °C to 100 °C?

given formula

V(T) =V₀ (1 + 0.18182 x 10⁻³T + 0.0078 x 10⁻⁶T²

Answer 1

The volume of mercury at 100°C is approximately 0.570 ft³. The change in height of the mercury when heated from 20°C to 100°C is approximately 0.010 ft³.

Step-by-step explanation:

The volume of mercury can be calculated using the formula:

V(T) = V₀ (1 + 0.18182 x 10⁻³T + 0.0078 x 10⁻⁶T²

Let's calculate the volume of mercury at 100°C:

V(100) = 0.560 ft³ (1 + 0.18182 x 10⁻³(100) + 0.0078 x 10⁻⁶(100)²

V(100) = 0.560 ft³ (1 + 0.018182 + 0.0000078)

V(100) = 0.560 ft³ (1.0181898)

V(100) ≈ 0.570 ft³

The volume of mercury at 100°C is approximately 0.570 ft³.

For the second part of the question, we can use the same formula to calculate the change in volume based on the change in temperature.

Let's calculate the change in height of the mercury when heated from 20°C to 100°C, assuming it is contained in a cylinder with a diameter of 0.25 in:

V(20) = πr²h

V(100) = πr²h'

Using the formula:

V(T) = V₀ (1 + 0.18182 x 10⁻³T + 0.0078 x 10⁻⁶T²

We can calculate the change in height by subtracting the initial height from the final height:

Change in height = h' - h

Change in height = V(100) - V(20)

Change in height = (0.560 ft³ (1 + 0.18182 x 10⁻³(100) + 0.0078 x 10⁻⁶(100)²) - (0.560 ft³ (1 + 0.18182 x 10⁻³(20) + 0.0078 x 10⁻⁶(20)²)

Change in height = (0.560 ft³ (1 + 0.018182 + 0.0000078) - (0.560 ft³ (1 + 0.0036364 + 0.00000156)

Change in height ≈ 0.560 ft³ (1.0181898) - 0.560 ft³ (1.00363796)

Change in height ≈ 0.570 ft³ - 0.560 ft³

Change in height ≈ 0.010 ft³

The change in height of the mercury when heated from 20°C to 100°C is approximately 0.010 ft³.