To find the correct atmospheric pressure at 27 degrees Celsius using the barometer reading, we need to account for the thermal expansion of the brass scale. The barometer reads 75 cm at 27 degrees Celsius, but since the scale expands with temperature, we must adjust this reading to get the accurate atmospheric pressure.
Understanding Thermal Expansion
When materials like brass are heated, they expand. This expansion can affect measurements taken with instruments made from those materials. The coefficient of linear expansion (α) tells us how much a material will expand per degree of temperature change. In this case, the coefficient for brass is given as 2 x 10^-5 per degree Celsius.
Calculating the Expansion
First, we need to determine how much the brass scale expands at 27 degrees Celsius. The formula for linear expansion is:
Where:
- ΔL = change in length
- L0 = original length (75 cm)
- α = coefficient of linear expansion (2 x 10^-5 /°C)
- ΔT = change in temperature from a reference point (0°C to 27°C, so ΔT = 27°C)
Plugging in the values:
- ΔL = 75 cm × (2 x 10^-5 /°C) × 27°C
Calculating this gives:
- ΔL = 75 cm × 2 x 10^-5 × 27 = 0.0405 cm
Adjusting the Barometer Reading
Now, we need to adjust the barometer reading to account for this expansion. The actual length of the barometer scale at 27 degrees Celsius is:
- L_actual = L_measured - ΔL
Substituting the values:
- L_actual = 75 cm - 0.0405 cm = 74.9595 cm
Calculating Atmospheric Pressure
Next, we can convert this length into atmospheric pressure. The standard atmospheric pressure at sea level is defined as 76 cm of mercury (Hg). The pressure can be calculated using the ratio of the actual barometric height to the standard height:
- P = (L_actual / 76 cm) × 101325 Pa
Where 101325 Pa is the standard atmospheric pressure in pascals. Plugging in the values:
- P = (74.9595 cm / 76 cm) × 101325 Pa
Calculating this gives:
Final Result
Thus, the correct atmospheric pressure at 27 degrees Celsius, after accounting for the thermal expansion of the brass scale, is approximately 98,000 pascals, or about 98 kPa. This adjustment is crucial for accurate readings in meteorological applications.
