The constant volume thermometer depicted below consists of a U-shaped tube fille

Question

The constant volume thermometer depicted below consists of a U-shaped tube filled with mercury which is open to the atmosphere on one side, and attached to a gas reservoir on the other side. When the gas in the reservoir is at temperature T_i the top of the two arm of mercury are at equal heights (h = 0 in the illustration). The temperature of the gas is then increased by Delta T = 65.4K, causing the difference in heights between the two mercury arms (h) to increase as illustrated. Assuming rho _mercury = 13.56 g/cm^3, T_i = 227.0K, and the volume of the reservoir V does not change mercury significantly, what is the change in height h? Answer in centimeters.

Explanation / Answer

from the given data

Ti = 227 K

Pi = Patm = 1 atm = 1.013*10^5 pa

Tf = 227 + 65.4

= 292.4 K

let Pf is the final pressure.

At constant volume, P/T = constant

Pf/Tf = Pi/Ti

Pf = Pi*(Tf/Ti)

= 1.013*10^5*(292.4/227)

= 1.30485*10^5 pa

now use, gauge prssure inside the rervoir,

P_gauge = Pf - Patm

rho_mercury*g*h = Pf - Patm

h = (Pf - Patm)/(rho_mercury*g)

h = (1.30485*10^5 - 1.013*10^5)/(13560*9.8)

h = 0.2196 m

= 0.220 (when rounded to two signiifcant figures)

= 22.0 cm

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