The mercury manometer shown in the figure is attached to a gascell. The mercury

Question

The mercury manometer shown in the figure is attached to a gascell. The mercury height h is 100 mm when the cell isplaced in an ice-water mixture. The mercury height drops to20 mm when the device is carried into an industrialfreezer What is the freezer temperature (oC)? (Hint: The right tube of the manometer ismuch narrower than the left tube. What reasonable assumption canyou make about the gas volume?) What is the freezer temperature (oC)? (Hint: The right tube of the manometer ismuch narrower than the left tube. What reasonable assumption canyou make about the gas volume?)

Explanation / Answer

P1 V1 / T1 = P2V2 / T2 Obviously, the gas volume will not change much. So T2 = P2 T1 / P1 Since the change in height of the Hg in the left tube isalso to be considered negligble the change in pressure is due to the change in height of the Hg inthe right tube. P2 / P1 = g h2 /( g h1) = h2 / h1 = 80 / 100= .8 T2 = .8 T1 = .8 * 273 = 218 deg K = -55deg C Since the change in height of the Hg in the left tube isalso to be considered negligble the change in pressure is due to the change in height of the Hg inthe right tube. P2 / P1 = g h2 /( g h1) = h2 / h1 = 80 / 100= .8 T2 = .8 T1 = .8 * 273 = 218 deg K = -55deg C

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