Published by:
CGP EDU Academic Team
Published on: September 12, 2026
The brass scale of a barometer gives correct reading at 0º C. Coefficient of thermal expansion of brass is 0.00002/º C. The barometer reads 75 cm at 27º C. What is the correct atmospheric pressure at 27ºC?
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Understand that the reading of the barometer increases due to the thermal expansion of the brass scale as temperature increases from 0ºC to 27ºC.
Step 2: The change in length due to thermal expansion can be calculated using the formula:
$$ L = L_0 (1 + \alpha \Delta T) $$
where $L_0$ is the original length (75 cm), $\alpha$ is the coefficient of thermal expansion (0.00002/ºC), and $\Delta T$ is the change in temperature (27ºC - 0ºC = 27ºC).
Step 3: Calculate the new effective length of the barometer:
$$ L = 75(1 + 0.00002 \times 27) $$
Simplifying this:
$$ L = 75(1 + 0.00054) $$
$$ L = 75(1.00054) $$
$$ L \approx 75.0405 \text{ cm} $$
Step 4: Using the barometric formula, we can relate the height of the mercury column to atmospheric pressure P:
$$ P = \rho g h $$
where ρ is the density of mercury (approximately 13.6 g/cm³), g is the acceleration due to gravity (approximately 980 cm/s²), and h is the height of the mercury column (75.0405 cm).
Step 5: Now substituting values:
$$ P = 13.6 \times 980 \times 75.0405 $$
Performing the calculation gives:
$$ P \approx 13388.8 \text{ dynes/cm}^2 = 133.888 \text{ kPa} $$
Therefore, the correct atmospheric pressure at 27ºC is approximately 133.888 kPa.
Step 2: The change in length due to thermal expansion can be calculated using the formula:
$$ L = L_0 (1 + \alpha \Delta T) $$
where $L_0$ is the original length (75 cm), $\alpha$ is the coefficient of thermal expansion (0.00002/ºC), and $\Delta T$ is the change in temperature (27ºC - 0ºC = 27ºC).
Step 3: Calculate the new effective length of the barometer:
$$ L = 75(1 + 0.00002 \times 27) $$
Simplifying this:
$$ L = 75(1 + 0.00054) $$
$$ L = 75(1.00054) $$
$$ L \approx 75.0405 \text{ cm} $$
Step 4: Using the barometric formula, we can relate the height of the mercury column to atmospheric pressure P:
$$ P = \rho g h $$
where ρ is the density of mercury (approximately 13.6 g/cm³), g is the acceleration due to gravity (approximately 980 cm/s²), and h is the height of the mercury column (75.0405 cm).
Step 5: Now substituting values:
$$ P = 13.6 \times 980 \times 75.0405 $$
Performing the calculation gives:
$$ P \approx 13388.8 \text{ dynes/cm}^2 = 133.888 \text{ kPa} $$
Therefore, the correct atmospheric pressure at 27ºC is approximately 133.888 kPa.
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