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# assign01 - difference between the room and the beer The...

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SYSC 3600 – Assignment #1 1/. Plutonium-239 is unstable and decays into Uranium-235.The decay rate is proportional to the amount of Plutomium-239 remaining. If we let p represent the amount of Plutonium-239 present, the following equation applies: kp p = Plutonium-239 has a half life of 24,100 years. This means that, if we begin with some amount of Plutonium-239, half it will be left after 24,100 years. Assuming that we begin with 100g of Plutonium-239, what is p(t) (the amount of Plutonium-239 present as a function of time ) ? What is the value of k ? What is the time constant of the system? Be sure to give units for p(t) , t , k , and the time constant. Hint: is this system analogous to any of the examples in part 1 of the notes? 2/. Consider a can of beer removed from a fridge. Assuming that the room is warmer than the fridge, heat will flow into the beer. The heat transfer rate is proportional to the overall heat transfer coefficient for the can, the area of the can, and the temperature

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Unformatted text preview: difference between the room and the beer. The heat flowing into the can will cause the beer to get warmer. The rate at which the beer will get warmer depends upon the heat transfer rate, the mass of beer present, and the specific heat of the beer (the amount of heat required to make a unit mass of beer one degree C warmer). Using the symbols given below, derive an equation relating the temperature of the beer ( T B ) to the temperature of the room ( T R ). Assume that the thickness of the can be neglected. U = overall heat transfer coefficient (in kJ per second per m 2 of can area per degree C) h = height of can (in m) d = diameter of can (in m) ρ = density of beer (in kg/m 3 ) c p = specific heat of beer (in kJ per kg per degree C) Is this system analogous to any of the examples in part 1 of the notes? 3/. Derive the defining equation for the system shown below: 4/. For the op-amp circuit shown below, derive an expression for V OUT in terms of V IN ....
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assign01 - difference between the room and the beer The...

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