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sukhopar [10]
2 years ago
15

It has been suggested that the surface melting of ice plays a role in enabling speed skaters to achieve peak performance. Carry

out the following calculation to test this hypothesis. At 1 atm pressure the density of ice is 920 kg m-3 , and the density of liquid water is 997 kg m-3. What pressure is required to lower the melting temperature by 4 C?
Chemistry
1 answer:
vesna_86 [32]2 years ago
5 0

Explanation:

Relation between pressure, latent heat of fusion, and change in volume is as follows.

          \frac{dP}{dT} = \frac{L}{T \times \Delta V}

Also, \frac{L}{T} = \Delta S^{fusion}_{m}

where, \Delta V^{fusion}_{m} is the difference in specific volumes.

Hence,    \frac{dP}{dT} = \frac{\Delta S^{fusion}_{m}}{\Delta V^{fusion}_{m}}

As, \Delta S^{fusion}_{m} = \frac{L}{T} = \frac{6010}{273.15} = 22.0 J/mol K

And,   \Delta V^{fusion}_{m} = \frac{M}{d_{H_{2}O}} - \frac{M}{d_{ice}} ...... (1)

where,    d_{H_{2}O} = density of water

              d_{ice} = density of ice

             M = molar mass of water = 18.02 \times 10^{-3} kg

Therefore, using formula in equation (1) we will calculate the volume of fusion as follows.

        \Delta V^{fusion}_{m} = \frac{M}{d_{H_{2}O}} - \frac{M}{d_{ice}}

                       = \frac{18.02 \times 10^{-3}}{997} - \frac{18.02 \times 10^{-3}}{920}  

                       = -1.51 \times 10^{-6}        

Therefore, calculate the required pressure as follows.

              \frac{dP}{dT} = \frac{22}{-1.51 \times 10^{-6}}

                              = 1.45 \times 10^{7} Pa/K

or,                           = 145 bar/K

Hence, for change of 1 degree pressure the decrease is 145 bar  and for 4.7 degree change dP = 145 \times 4.7 bar

                              = 681.5 bar

Thus, we can conclude that pressure should be increased by 681.5 bar to cause 4.7 degree change in melting point.

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