Question

A test tube contains 2.61x10⁻⁴ m³ of liquid carbon tetrachloride (β = 1240x10⁻⁶ (C°)⁻¹) at a temperature of 64.0°C. The test tube and the carbon tetrachloride are cooled to a temperature of -13.0°C, which is above the freezing point of carbon tetrachloride. Find the volume of carbon tetrachloride in the test tube at -13.0°C.

Answer 1

To find the final volume of carbon tetrachloride at -13.0°C using the volumetric thermal expansion coefficient, we calculate the change in temperature and apply the formula for volumetric expansion with the initial volume and expansion coefficient.

Step-by-step explanation:

The question pertains to the calculation of the volume of carbon tetrachloride at a different temperature using the volumetric thermal expansion coefficient. Given the initial volume (V1) of 2.61x10−4 m³ at an initial temperature (T1) of 64.0°C, we aim to find the final volume (V2) at a new temperature (T2) of -13.0°C.

The volumetric thermal expansion coefficient (β) for carbon tetrachloride is given as 1240x10−6 (C°)−1. To do so, we'll use the formula for volumetric expansion V2 = V1 [1 + β(T2 - T1)].

Firstly, we need to calculate the change in temperature, ΔT = T2 - T1, which is -13.0°C - 64.0°C = -77.0°C. Then we apply the change in temperature to the formula:
V2 = 2.61x10−4 m³ [1 + (1240x10−6 (C°)−1) (-77.0°C)].
By calculating V2, we'll find the final volume of carbon tetrachloride at -13.0°C.