Coefficient of real expansion of mercury is 0.18 × 10–3/°C. If the density of mercury at 00C is 13.6 gm/cc., its density at 573 K will be

To solve this problem, we need to use the formula for the change in density due to thermal expansion. The formula is:

Δρ = ρ0 * β * ΔT

where:

• Δρ is the change in density,
• ρ0 is the initial density,
• β is the coefficient of volume expansion, and
• ΔT is the change in temperature.

However, we are given the coefficient of linear expansion (α), not the coefficient of volume expansion (β). For most substances, β is approximately equal to 3α, so we can use this relationship to find β.

First, let's find β:

β = 3α = 3 * 0.18 × 10–3/°C = 0.54 × 10–3/°C

Next, we need to convert the final temperature from Kelvin to Celsius, because our coefficient of expansion is in terms of Celsius. The conversion is:

T (°C) = T (K) - 273.15

So, the final temperature in Celsius is:

573 K - 273.15 = 299.85 °C

Now, we can find the change in density:

Δρ = ρ0 * β * ΔT = 13.6 gm/cc * 0.54 × 10–3/°C * 299.85 °C = 2.21 gm/cc

Finally, we subtract this change from the initial density to find the final density:

ρ = ρ0 - Δρ = 13.6 gm/cc - 2.21 gm/cc = 11.39 gm/cc

So, the density of mercury at 573 K is approximately 11.39 gm/cc.