Question

An Insulated tube is filled with a large number n of lead spheres, each of mass m. The tube is inverted s times so that the spheres completely fall through an average distance L each time. The temperature of the spheres is measured before and after the inversions and the resultant change in temperature of delta T

What is the specific heat capacity of lead?

Answer 1

we have an insulating tube which means no heat can leave or enter to it as we invert tube s time each time we give some amount of mechanical energy to the lead spheres and that energy would convert into heat energy that energy would raise the temperature of the spheres

mass of each sphere= m

number of sphere=n

tube is inverted= "s" times

change in temperature = dT

average distance fall=L

mechanical energy given on each inversion= MgL

M= total mass of spheres= n.m

g=acceleration due to gravity

so mechanical energy given each time = n.m.g.L

in s inversion total energy given= s.m.n.g.L Joules...................................1

this total energy would convert into heat energy and thus raise the temperature of spheres

heat energy= M.C.dT.............................................2

C- specific heat of lead

equating equation 1 and 2

M.C.dT= s.m.n.g.L ( as m.n=M)

C = (s.g.L)/dT jouls/kg { specific heat of lead}