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A barometer reads 75cm on steel scale when room temperature is 30 degree Celsius. The scale is graduated at 0 degree Celsius. Find correct atmospheric pressure if coefficient of linear expansion of steel=10^-5(10 raise to power -5)/C and coefficient of volumetric expansion of mercury is 1.8*10^-3 /C
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Most Upvoted Answer
A barometer reads 75cm on steel scale when room temperature is 30 degr...
Given:
- Room temperature (T1) = 30°C
- Barometer reading on steel scale (H1) = 75 cm
- Coefficient of linear expansion of steel (αsteel) = 10^-5 /°C
- Coefficient of volumetric expansion of mercury (βmercury) = 1.8 * 10^-3 /°C

To Find:
- Correct atmospheric pressure

Formula:
The relationship between the change in height of a liquid column in a barometer and the change in temperature is given by:
ΔH = H2 - H1 = βL(T2 - T1)
Where,
ΔH = Change in height of liquid column
H2 = Final height of liquid column
H1 = Initial height of liquid column
βL = Coefficient of linear expansion of liquid
T2 = Final temperature
T1 = Initial temperature

Approach:
1. Convert the given barometer reading from the steel scale to the mercury scale.
2. Use the given coefficient of linear expansion of steel to find the change in height of the liquid column due to the change in temperature.
3. Convert the change in height back to the steel scale using the coefficient of volumetric expansion of mercury.
4. Calculate the correct atmospheric pressure.

Calculation:
1. Conversion to Mercury Scale:
The length of the mercury column at 0°C is 76 cm on the steel scale. Since the steel scale is graduated at 0°C, the mercury column reading on the steel scale is the same as on the mercury scale at 0°C.

2. Change in Height of Liquid Column:
Using the formula, ΔH = H2 - H1 = βL(T2 - T1)
ΔH = (H2 - H1) / βL = (76 - 75) / (10^-5) = 10^5 cm/°C

3. Conversion back to Steel Scale:
The change in height of the liquid column is in mercury scale units. To convert it back to the steel scale units, we divide by the coefficient of volumetric expansion of mercury:
ΔH' = ΔH / βmercury = 10^5 cm/°C / (1.8 * 10^-3 /°C) = 5.56 * 10^7 cm/°C

4. Calculation of Correct Atmospheric Pressure:
The atmospheric pressure can be calculated by subtracting the change in height from the initial barometer reading:
P = H1 - ΔH' = 75 cm - 5.56 * 10^7 cm/°C = -5.56 * 10^7 cm/°C

Answer:
The correct atmospheric pressure is -5.56 * 10^7 cm/°C.
Community Answer
A barometer reads 75cm on steel scale when room temperature is 30 degr...
74.89cm
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The atmospheric lapse rateFor small volumes of gas, according to kinetic theory of gases, all parts of the gas are at the same temperature. But for huge volumes of gas like atmosphere, assumption of a uniform temperature throughout the gas is not valid. Different parts of the atmosphere are at different temperatures. Apart from the surface of the earth, variations also occur in temperature at different heights in the atmosphere.The decrease in temperature with height called the atmospheric lapse rate is similar at various locations across the surface of the Earth. By analyzing the data collected at various locations, it is found that average global lapse rate is – 6.7 °C/Km.The linear decrease with temperature only occurs in the lower part of the atmosphere called the troposphere. This is the part of the atmosphere in which weather occurs and our planes fly. Above the troposphere is the stratosphere, with an imaginary boundary separating the two layers. In the stratosphere, temperature tends to be relatively constant.Absorption of sunlight at the Earth’s surface warms the troposphere from below, so vertical convection currents are continually mixing in the air. As a parcel of air rises, its pressure drops and it expands. The parcel does work on its surrounding, so that its internal energy and therefore, its temperature drops. Assume that the vertical mixing is so rapid as to be adiabatic and the quantityTP(1 – λ)/λ has a uniform value through the layers of troposphere.(M is molecular mass of the air, R is universal gas constant, g is gravitational acc., P and T are pressure and temperature respectively at the point under consideration and y is height.)Q. The value of theoretical lapse rate on the earth is (use g = 9.8 m/s2 ; R = 8.3 J/mol-k and M = 29 g/mol)

The atmospheric lapse rateFor small volumes of gas, according to kinetic theory of gases, all parts of the gas are at the same temperature. But for huge volumes of gas like atmosphere, assumption of a uniform temperature throughout the gas is not valid. Different parts of the atmosphere are at different temperatures. Apart from the surface of the earth, variations also occur in temperature at different heights in the atmosphere.The decrease in temperature with height called the atmospheric lapse rate is similar at various locations across the surface of the Earth. By analyzing the data collected at various locations, it is found that average global lapse rate is – 6.7 °C/Km.The linear decrease with temperature only occurs in the lower part of the atmosphere called the troposphere. This is the part of the atmosphere in which weather occurs and our planes fly. Above the troposphere is the stratosphere, with an imaginary boundary separating the two layers. In the stratosphere, temperature tends to be relatively constant.Absorption of sunlight at the Earth’s surface warms the troposphere from below, so vertical convection currents are continually mixing in the air. As a parcel of air rises, its pressure drops and it expands. The parcel does work on its surrounding, so that its internal energy and therefore, its temperature drops. Assume that the vertical mixing is so rapid as to be adiabatic and the quantityTP(1 – λ)/λ has a uniform value through the layers of troposphere.(M is molecular mass of the air, R is universal gas constant, g is gravitational acc., P and T are pressure and temperature respectively at the point under consideration and y is height.)Q. If behaviour of the mixing of parcels of air is approximately assumed to be adiabatic then lapse rate can be expressed as

The atmospheric lapse rateFor small volumes of gas, according to kinetic theory of gases, all parts of the gas are at the same temperature. But for huge volumes of gas like atmosphere, assumption of a uniform temperature throughout the gas is not valid. Different parts of the atmosphere are at different temperatures. Apart from the surface of the earth, variations also occur in temperature at different heights in the atmosphere.The decrease in temperature with height called the atmospheric lapse rate is similar at various locations across the surface of the Earth. By analyzing the data collected at various locations, it is found that average global lapse rate is – 6.7 °C/Km.The linear decrease with temperature only occurs in the lower part of the atmosphere called the troposphere. This is the part of the atmosphere in which weather occurs and our planes fly. Above the troposphere is the stratosphere, with an imaginary boundary separating the two layers. In the stratosphere, temperature tends to be relatively constant.Absorption of sunlight at the Earth’s surface warms the troposphere from below, so vertical convection currents are continually mixing in the air. As a parcel of air rises, its pressure drops and it expands. The parcel does work on its surrounding, so that its internal energy and therefore, its temperature drops. Assume that the vertical mixing is so rapid as to be adiabatic and the quantityTP(1 – λ)/λ has a uniform value through the layers of troposphere.(M is molecular mass of the air, R is universal gas constant, g is gravitational acc., P and T are pressure and temperature respectively at the point under consideration and y is height.)Q. Mechanical equilibrium of the atmosphere requires that the pressure decreases with altitude according to . Assuming free fall acceleration to be uniform, then lapse rate is given by

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A barometer reads 75cm on steel scale when room temperature is 30 degree Celsius. The scale is graduated at 0 degree Celsius. Find correct atmospheric pressure if coefficient of linear expansion of steel=10^-5(10 raise to power -5)/C and coefficient of volumetric expansion of mercury is 1.8*10^-3 /C
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A barometer reads 75cm on steel scale when room temperature is 30 degree Celsius. The scale is graduated at 0 degree Celsius. Find correct atmospheric pressure if coefficient of linear expansion of steel=10^-5(10 raise to power -5)/C and coefficient of volumetric expansion of mercury is 1.8*10^-3 /C for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A barometer reads 75cm on steel scale when room temperature is 30 degree Celsius. The scale is graduated at 0 degree Celsius. Find correct atmospheric pressure if coefficient of linear expansion of steel=10^-5(10 raise to power -5)/C and coefficient of volumetric expansion of mercury is 1.8*10^-3 /C covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A barometer reads 75cm on steel scale when room temperature is 30 degree Celsius. The scale is graduated at 0 degree Celsius. Find correct atmospheric pressure if coefficient of linear expansion of steel=10^-5(10 raise to power -5)/C and coefficient of volumetric expansion of mercury is 1.8*10^-3 /C.
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