the heart of a man pumps 4 litres of blood per minute at a pressure of 130 mm of mercury. If the density of mercury is 13.6 g/cm^-3, then calculate the power of the heart. (assume g=10m/s)

ANSWER WITH DETAILED SOLUTION N EXPLANATION

WORK DONE W IS GIVEN BY



W = F.D



F = PA (PRESSURE X AREA)



OR W = P A.D = P (AD) = P V



OR WORK DONE = PRESSURE X VOLUME



HERE PRESSURE P = 130mm OF Hg = 10⁵ * 130/760

OR P = 13 x 10⁵ / 76 Pa

VOLUME V = 4L = 4000 cm³ = 4x10^-3 m³



HENCE W = PV = (13 x 10⁵ / 76 ) x 4x10^-3



OR Wok done  = 68.42 JOULES



NOW THE PUMPING OF 4 L OF BLOOD IS DONE IN 1min = 60s



THUS POWER = WORK DONE/TIME



OR POWER = 68.42/60 = 1.1403 WATTS

Volume=areaXlength,when Force F is applied to move blood through length l in its direction,W=F.l,but F=P.A and hence,W=P.(A.l)=P.V

this is the derivation