A glass is filled to the mark with60cm³of mercury at 20°C if the flask and its content are heated at 40°C how much Mercury will be above the mark

Answer 1

To determine how much mercury will be above the mark when the glass and its contents are heated to 40°C, we first need to find the expansion coefficient of the mercury and the glass.

The coefficient of volume expansion for mercury is 180x10^(-6) ¹/°C, and the glass's coefficient is 27x10^(-6) ¹/°C.

Now, let's find the volume expansion for both the mercury and the glass.

ΔV_Mercury = Initial volume x coefficient x ΔT
ΔV_Mercury = 60 cm³ x 180x10^(-6) ¹/°C x (40°C - 20°C)
ΔV_Mercury = 60 cm³ x 180x10^(-6) ¹/°C x 20°C
ΔV_Mercury = 0.00324 cm³

Let us assume the initial volume of the flask is V cm³ (up to the mark). Now, we will find the volume expansion for the glass (flask).

ΔV_Glass = Initial volume x coefficient x ΔT
ΔV_Glass = V cm³ x 27x10^(-6) ¹/°C x (40°C - 20°C)
ΔV_Glass = V cm³ x 27x10^(-6) ¹/°C x 20°C
ΔV_Glass = V cm³ x 0.00054 cm³/cm³

Since we are only interested in the change in mercury's level, we can set up the following equation:

0.00324 cm³ - V cm³ x 0.00054 cm³/cm³ = ΔV_AboveMark

However, we don't have the initial volume of the flask, V. In real-world scenarios, the volume of the flask is usually much larger than the volume of mercury filled into it (60 cm³). Considering this, the expansion of the glass will have a much smaller impact compared to the expansion of the mercury.

Thus, we can approximate the change in mercury's level with the expansion of the mercury:

ΔV_AboveMark ≈ ΔV_Mercury = 0.00324 cm³

So, approximately 0.00324 cm³ of mercury will be above the mark when the flask and its content are heated to 40°C.