At a temperature of 24.20DegreeC the hole in a steel plate has a diameter of 1.0

Question

At a temperature of 24.20DegreeC the hole in a steel plate has a diameter of 1.060 cm. If a steel rod with a diameter of 1.068 cm has to just slip through this hole, to what temperature should the plate be heated? The coefficient of area expansion of steel is 24 Times 10^minus6/DegreeC. If a 520 mL ordinary glass beaker is filled to the brim with ethyl alcohol at a temperature of 5.60DegreeC, how much will overflow when their temperature reaches 22.0DegreeC? How much less water would overflow under the same conditions? Calculate the number of moles in the 1.60 L volume of air in the lungs of the average person. Note that the air is at 37.0DegreeC (body temperature) and atmospheric pressure.

Explanation / Answer

5.solution

Assuming that the volume of the beaker remains constant, because the volume extension for a
rigid material is much smaller than for a liquid.

use
V = v0(1 + *T) where is the volume temperature extension coefficient
for ethyl alcohol = 1.4*10^-3 K^-1
for water = 0.206*10^-3 K^-1

a) V = v0(1 + *T)


Vt = 520 [ 1 + 1.4*10-3 ( 22 - 5.6 )] = 531.93 mL
overflow at 22°C = 11.93 mL


b) Water = 0.206*10-3 /°C
520 [ 1 + 0.206*10-3 ( 22 - 5.6 )] = 521.75 mL
overflow at 22°C = 1.75 mL

6.soltuion

.Assuming you mean 1 atm.... PV=nRT

where n is moles
R is the gas constant 0.0821
T is Temp
P is your 1atm
and V is volume 1.60 L

solve for n.....n=(PV)/(RT)

n = 1atm*1.60L / 0.0821*37 = 5.26*10-1 mol

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