Question

As shown in Figure Q6a, a solid metallic sphere of mass m = 0.1 kg, initial temperature T1 = 307 K and initial velocity v1 = 2 m/s is allowed to fall from an initial height of z1 = 1.6 m. The specific heat capacity of the sphere material, c, is a linear function of temperature T, c = aT + b (in J/kg/K), where a and b are constants of value 3.4 and 503, respectively. By the time the sphere has descended to its final height z2 = 0 m, its final temperature is T2 = 447 K. Calculate the size of that heat transfer interaction experienced by the sphere Q12 (in J) during its descent. You may assume a value of g = 9.81 m/s2.

Figure Q6a Solid metallic sphere m, c=aT+b v1, z1, T1 — v1, z1, T1

Answer 1

* from est law of twonmodynamics! 0 12 = AEiz + Wiloz --- (1) here, ar2 = heat interaction AE1-z = total Enoyy change. - CAU)-2 + Lokehz + LAP.E)-2 Wi-2 = work interaction. here, • Change in intonal Energy, San a medo (AV)e2 = m S. (QTtbat cowione e m are +br) Cauli-2 = m* [ Şx (T-172) +b(T2-T7 (OU21-2 = 0.1* 794 -[(4972-(30)} + 503*2447-307}] (AU) 1-2 0-1 (AV) 1-2 -29987.2 Joule • Change in kinetic Energy CAKE)-2 = možemvis berita Immx (VŽ-11) 01* [1092-(2)] verwrity at a en not given. tience, Consider, CAKE)-2-0.2 Joue

* change in potential Enegre COPE)j-2 = mg[zz-,) = 0.1* 9.81 # (0-1-6) 1-1.5696 Joule work, wi-2=0 { from cancis} Q2-2 = 29987.2 -0.2 - 1.5696 to -91-2= 2498504 João