Question

The hunting pellets (amount of mass = 1kg) are poured into a long vertical tube (a cross section A=10cm^2). These pellets are fell with uniform motion. Calculate the change of temperature in the central part of the tube. Specific heat of the glycerin c=2400J/kgK and its density is 1200kg/m^3. Assume that these pellets have negligible heat capacity.

Hey, I dunno how to solve it :<

Answer 1

since the pellets are fell with uniform motion so it means the workdone by gravity (which should increase the speed / kinetic energy of pellet)on pellet is being stored as heat

let the length of vertical tube be L so workdone by gravity when pellet reaches at central part of tube

$W=m_{p}g\frac{L}{2}$

the volume of gycerine

V= 0.5AL

$W=V \rho S \Delta T \Rightarrow A\frac{L}{2} \rho S \Delta T=m_{p}g\frac{L}{2}$

$\Rightarrow \Delta T=\frac{m_{p}g}{A\rho S}$

$\Rightarrow \Delta T=3.4*10^{-3}K$