Thermodynamics?

Question

(a) A sample of liquid water of mass of 10 g and a temperature 20°C is placed into a large thermally insulated vessel containing steam at 100°C.

How much water will be present when equilibrium is achieved?

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(b) A glass flask whose volume is 1000.0 cm^3 at 0.0 ºC is completely filled with mercury at this temperature. When the flask and mercury are warmed to 55 ºC, 8.45 cm^3 of mercury overflow.

If the coefficient of volume expansion of mercury is
1.82 × 10^(-4) K^(-1) , compute the coefficient of volume expansion of the glass.

Thanks in advance for all the help :)

Answer 1

a) 800 calories will be needed to heat that 10 g of water to 100 C and so a small amount of water is condensed from the steam to provide the heat since the system is themodynamically insulated. The latent heat of water - steam is 540 calories and so 800 / 540 = 40/27 = 1.5 grams approximately and the total quantity of water will be 11.5 grams app.

b) I am not doing the problem but will suggest that you multiply the coefficient of expansion of mercury with the temperature difference of 55 degrees and subtract the volume of mercury that has overflown. The difference divided by 55 will give the coefficient of expansion of glass.

Answer 2

For problem (a):

All that we can say for sure is that more than 10 g of liquid water will be present.

Since you did not specify:

How much steam was present,
The initial internal temperature of the vessel or
The pressure within the vessel...

All we can say for sure is that some of the water in vaporous state (steam) will be condensed into liquid.

A "thermally insulated vessel" only means that no heat escapes from the vessel itself. It does not mean that the internal temperature of the vessel itself does not change (especially if it is a multi-chambered vessel such as a thermos/vacuum bottle.)

For problem (b)

We would probably need to know the shape of the flask, the mass of the glass and the volume of the glass, not just the internal volume of the container.

For scientific glass the coefficient of expansion is usually given in the specifications of the glass. Just look it up:
e.g.; B270 Crown Glass - ((0/300°C): 95 X 10^-7/°C)

If it is not scientific glass, the coefficient of expansion may not be uniform due to inconsistency in density and imperfections in the glass.
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