A mercury barometer reads 75.0 cm when measured with a steel scale. The steel scale is graduated correctly at 0 deg C, but the room temperature is 30 deg C. Steel has linear expansion coefficient alpha = 1.2*10⁻⁵ per deg C and mercury has volume expansion coefficient gamma = 1.8*10⁻⁴ per d

Question

A mercury barometer reads 75.0 cm when measured with a steel scale. The steel scale is graduated correctly at 0 deg C, but the room temperature is 30 deg C. Steel has linear expansion coefficient alpha = 1.2*10⁻⁵ per deg C and mercury has volume expansion coefficient gamma = 1.8*10⁻⁴ per deg C. The corrected atmospheric pressure (in cm of Hg) is closest to:

Accepted Answer

74.6. At 30 deg C the steel scale's divisions are longer than nominal, so each marked centimeter actually spans (1 + alpha*dT) cm; thus true length = 75*(1 + alpha*dT). But pressure must be quoted as the height of an equivalent column of mercury at 0 deg C; mercury at 30 deg C is less dense, so the equivalent 0 deg C height is the true length divided by (1 + gamma*dT). Net correction factor (1 + alpha*dT - gamma*dT).

Solution

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