If a thermometer contained a gram of mercury, how much would the volume of the mercury change when the temperature rose from 0 degrees to 30 degrees Centigrade? From 30 degrees to 60 degrees? From 60 degrees to 90 degrees? From 90 degrees to 120 degrees?
To calculate the change in volume of mercury in a thermometer with temperature variations, we need to use the coefficient of volume expansion of mercury. The coefficient of volume expansion (β) represents the fractional change in volume per degree Celsius change in temperature.
For mercury, the coefficient of volume expansion (β) is approximately 0.181 x 10^(-3) per degree Celsius.
To calculate the change in volume, we can use the formula:
ΔV = V * β * ΔT
where:
ΔV is the change in volume
V is the initial volume
β is the coefficient of volume expansion
ΔT is the change in temperature in degrees Celsius
Let's calculate the change in volume for each temperature range:
1. From 0 degrees to 30 degrees Celsius:
ΔT = 30 - 0 = 30 degrees Celsius
ΔV = V * β * ΔT = 1 gram * 0.181 x 10^(-3) per degree Celsius * 30 degrees Celsius = 0.00543 grams
2. From 30 degrees to 60 degrees Celsius:
ΔT = 60 - 30 = 30 degrees Celsius
ΔV = V * β * ΔT = 1 gram * 0.181 x 10^(-3) per degree Celsius * 30 degrees Celsius = 0.00543 grams
3. From 60 degrees to 90 degrees Celsius:
ΔT = 90 - 60 = 30 degrees Celsius
ΔV = V * β * ΔT = 1 gram * 0.181 x 10^(-3) per degree Celsius * 30 degrees Celsius = 0.00543 grams
4. From 90 degrees to 120 degrees Celsius:
ΔT = 120 - 90 = 30 degrees Celsius
ΔV = V * β * ΔT = 1 gram * 0.181 x 10^(-3) per degree Celsius * 30 degrees Celsius = 0.00543 grams
Therefore, for each temperature range, the change in volume of the mercury in the thermometer is approximately 0.00543 grams.