A 9 cm diameter sphere of plutonium is initially at a temperature of 90 C. It...

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A 9 cm diameter sphere of plutonium is initially at a temperature of 90 °C. It is placed in a very large water bath at time t = 0. The water bath is initially at a uniform temperature of 5 °C. The heat transfer coefficient is estimated to be 600 watts/(m 2 °C). The specific heat of plutonium is 134 Joule/ (kg °C) and its density is approximately 20 gram per cc. Ongoing nuclear decay due to the various plutonium isotopes percentages in this sphere creates heat at the rate of 3 W / kg. Estimate the time at which the average temperature of the sphere will be 45 °C. Use a method that assumes decay heat rate is small compared to the convection heat transfer is acceptable. Don't neglect the heat from radioactive decay completely in part b). a) First calculate the time without the radioactive decay heat. b) Then estimate the incremental time to transfer the additional heat (from decay) and reach the target temperature. HINT: determine the average heat transfer rate, during the cooldown process of part a). Then determine the additional time needed (at this average heat transfer rate) to remove c) Comment on whether the assumption that the decay heat rate is much smaller than the average conduction/convection heat transfer rate seems to be valid. A 9 cm diameter sphere of plutonium is initially at a temperature of 90 °C. It is placed in a very large water bath at time t = 0. The water bath is initially at a uniform temperature of 5 °C. The heat transfer coefficient is estimated to be 600 watts/(m 2 °C). The specific heat of plutonium is 134 Joule/ (kg °C) and its density is approximately 20 gram per cc. Ongoing nuclear decay due to the various plutonium isotopes percentages in this sphere creates heat at the rate of 3 W / kg. Estimate the time at which the average temperature of the sphere will be 45 °C. Use a method that assumes decay heat rate is small compared to the convection heat transfer is acceptable. Don't neglect the heat from radioactive decay completely in part b). a) First calculate the time without the radioactive decay heat. b) Then estimate the incremental time to transfer the additional heat (from decay) and reach the target temperature. HINT: determine the average heat transfer rate, during the cooldown process of part a). Then determine the additional time needed (at this average heat transfer rate) to remove c) Comment on whether the assumption that the decay heat rate is much smaller than the average conduction/convection heat transfer rate seems to be valid.

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In part a of the question we calculated the time it would take for the plutonium sphere to cool down from 90 C to 45 C without taking into account the heat generated by radioactive decay This means we ... View the full answer