A 50.00ml sample of mercury at room temperature (293.0K) is cooled. What is the volume of the sample when the mercury reaches 273.0K? The coefficient of volume expansion of mercury is 182.0 x 10-6 K-1.

The volume of the mercury sample at 273 K is 49.818 mL

Explanation:

Step 1: Data given

Volume at 293 K = 50.00 mL

The coefficient of volume expansion of mercury is 182.0 * 10^-6/K

Step 2: Calculate the new volume

ΔV = β*Vi*ΔT

⇒ with ΔV = the change in volume

⇒ with β = The coefficient of volume expansion of mercury is 182.0 * 10^-6/K

⇒ with Vi = the initial volume = 50.00 mL

⇒ with ΔT = the change in temperature = 20 K

ΔV = 182.0 * 10^-6/K * 50 * 20

ΔV = 0.182 L

This means the volume change is - 0.182 L

ΔV = V2 - V1

V2 = ΔV - V1

V2 = 50.00 mL - 0.182 = 49.818 mL

The volume of the mercury sample at 273 K is 49.818 mL