I Heart Energy

Energy output is equal to work done which in turn is equal to

$Force\times Displacement=Pressure\times Volume$

Hence, work done per second is:

$w=10^{4}\times 5\times \frac{10^{-3}}{60}=\frac{5}{6} Watts$

Hence, the energy output in $80$ years is:

$E=\frac{5}{6}\times 80 \times 365.25 \times 24 \times 3600=\boxed{2.1038\times 10^{9} J}$

Work done = Pressure x Volume

Hence, Work done/min = Pressure x Volume/min

$= 10^4$ $Pa$ x $\frac{5000}{1000000}$ $m^3/min$

$= 50$ $J/min$

$= 3000$ $J/hour$

$= 72000$ $J/day$

$= 26298000$ $J/year$

$= \boxed{2103840000}$ $J/80 years$

Using dimensional analysis, we know that $Pa= \frac{N}{m^2}$ ( $P=\frac{F}{A}$ ) and that $1 L = \frac{m^3}{1000}$ . Then, we see that $Pa \cdot L = N \cdot m = J$ . Thus, the heart's energy output is $\frac{5 \cdot 10^4}{1000} = 50 J$ per minute. Converting to 80 years yields: $50 \times 60 \times 24 \times 365.25 \times 80 = \boxed{2.104 \times 10^9}$

Let the surface area of the blood vessel (which we consider to be uniform throughout) be A.

V = Ad (Volume = A * distance) F = pA (Force = pressure * A) W = Fd = (pA)(V/A) = pV = pRt (where R is the flow rate).

Substituting, W = $10^{4} \times (5 \times 60 \times 24 \times 365.25 \times 80) / 1000 = 2103840000$

Firstly, we are given 2 important dats : change in volume and pressure. Hence from the equation

W=PdV

We can find the work done per second by plugging in the values for P and dV but we have to change 5L/min into cubic metres per second.

From W=PdV , W= $10^{4}\times 8.333^{-5}$

W=0.8333J

So the total energy output of their heart in Joules is $80\times365.25\times24\times3600\times0.8333$

= $\boxed{2.10^{9}}$ Joules

The solution comes out of the units. You want an answer in Joules, and a Joule is a Newton metre. You are given Pascals, and a Pascal is a Newton per metre cubed. You are also given litres, i.e. decimetres cubed, so you just need to flip that into metres cubed by X 10 E-3, then you can see that you just need to multiply pressure by flow and scale up from one minute to the lifetime.

J=Nm Pa=N/m2 J=m3*Pa;compute lifetime volume & multiply by E4 Pa.