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awais1985

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I was working on the following problem:

Determine the power output as a function of time from an energy storage device for a four hour discharge period when it is known that for this type of system the power is a linear function of time, (Power) = a0 - bt, where a0 = 1.1(105) W, b is a constant and t is the time. The energy stored in the device at the star of this process is 8.1(108) J. Using your result calculate the power delivered at 2.4 hours into the discharge process.

Solution:

What i did was integrate the power equation to come up with an energy equation since

energy is the integral of power w.r.t time. i got the following expression

Energy = Energy (at t=0) – (bt2)/2

Now we are given that At t=0; Energy = 8.1 × 108 J

t=1; Energy = 8.1 × 108 – b/2

t=2; Energy = 8.1 × 108 – 2b

t=3; Energy = 8.1 × 108 – 9b/2

t=4; Energy = 8.1 × 108 – 8b

At t=2.4; Energy =8.1 × 108 – 5.76b/2

I don't know how to calculate 'b' here. Am i doing it right or should i change my approach?

Determine the power output as a function of time from an energy storage device for a four hour discharge period when it is known that for this type of system the power is a linear function of time, (Power) = a0 - bt, where a0 = 1.1(105) W, b is a constant and t is the time. The energy stored in the device at the star of this process is 8.1(108) J. Using your result calculate the power delivered at 2.4 hours into the discharge process.

Solution:

What i did was integrate the power equation to come up with an energy equation since

energy is the integral of power w.r.t time. i got the following expression

Energy = Energy (at t=0) – (bt2)/2

Now we are given that At t=0; Energy = 8.1 × 108 J

t=1; Energy = 8.1 × 108 – b/2

t=2; Energy = 8.1 × 108 – 2b

t=3; Energy = 8.1 × 108 – 9b/2

t=4; Energy = 8.1 × 108 – 8b

At t=2.4; Energy =8.1 × 108 – 5.76b/2

I don't know how to calculate 'b' here. Am i doing it right or should i change my approach?

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