if a thermometer contained a gram of mercury, how much would the volume of the mercury change when the temperature rose from 0 degrees celcius to 30 degrees celcius?
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To determine the change in volume of the mercury in the thermometer, we need to use the coefficient of volume expansion of mercury.
The coefficient of volume expansion (β) for mercury is approximately 0.181 x 10^(-3) per degree Celsius. This means that for every degree Celsius change in temperature, mercury expands by 0.181 x 10^(-3) times its original volume.
Given:
Initial temperature (T1) = 0 degrees Celsius
Final temperature (T2) = 30 degrees Celsius
Initial volume (V1) = 1 gram
First, we need to calculate the change in temperature:
ΔT = T2 - T1 = 30°C - 0°C = 30°C
Now, we can calculate the change in volume using the formula:
ΔV = V1 * β * ΔT
ΔV = 1 gram * 0.181 x 10^(-3) per degree Celsius * 30°C
ΔV = 1 * 0.181 * 10^(-3) * 30
ΔV ≈ 0.0543 cubic centimeters
Therefore, the volume of the mercury in the thermometer would change by approximately 0.0543 cubic centimeters when the temperature rises from 0 degrees Celsius to 30 degrees Celsius.
To determine how much the volume of mercury would change in this scenario, we need to understand the concept of thermal expansion.
The expansion of a material when its temperature increases is governed by its coefficient of thermal expansion (α), which is a property specific to each substance. For mercury, its coefficient of thermal expansion is approximately 0.000181 per degree Celsius.
Now, let's calculate the change in volume using the formula:
ΔV = V * α * ΔT
ΔV represents the change in volume, V is the initial volume of mercury, α is the coefficient of thermal expansion for mercury, and ΔT is the change in temperature.
Given:
Initial temperature (T1) = 0 degrees Celsius
Final temperature (T2) = 30 degrees Celsius
Volume of mercury (V) = 1 gram (density of mercury is roughly 13.6 g/cm³)
First, convert the mass of mercury to its volume using its density:
V = m / ρ
V = 1 g / 13.6 g/cm³
V ≈ 0.0735 cm³
Now, calculate the change in volume:
ΔV = V * α * ΔT
ΔV = 0.0735 cm³ * 0.000181 / °C * (30 °C - 0 °C)
ΔV ≈ 0.000399 cm³
Therefore, the volume of the mercury would increase by approximately 0.000399 cm³ when the temperature rises from 0 degrees Celsius to 30 degrees Celsius.