Question

For mercury to expand its volume by 2%, what change in temperature is necessary?

a) Depends on initial temperature
b) 2%
c) Not enough information
d) Approximately 100°C

Answer 1

The temperature change required for mercury to expand its volume by 2% depends on the coefficient of volumetric expansion and the initial temperature. Without this information, we can only estimate an approximate temperature change by assuming an average coefficient.

Step-by-step explanation:

Determining the temperature change required for mercury to undergo a 2% expansion involves applying Charles's Law, which expresses the direct proportionality between the volume of a gas and its temperature at constant pressure. However, the absence of the initial temperature impedes the calculation of an exact value. To estimate the change, we typically rely on the coefficient of volumetric expansion for mercury. Unfortunately, the provided text lacks the specific coefficient necessary for a precise calculation.

Despite this limitation, we can offer a rough estimate by assuming an average volumetric expansion coefficient for mercury. This coefficient, which varies with temperature, represents the rate at which the volume of mercury changes per unit temperature increase.

The general formula for volumetric expansion is:

\[ \Delta V = V_0 \beta \Delta T \]

Here, \( \Delta V \) is the change in volume, \( V_0 \) is the initial volume, \( \beta \) is the volumetric expansion coefficient, and \( \Delta T \) is the temperature change.

Although the exact coefficient is missing, an approximate temperature change can be calculated using a reasonable average value for \( \beta \). However, for precise calculations, the specific coefficient at the relevant temperature range would be required.