Number 7 6. We presented the full solution of the vibrating rectangular membranein Equation 6.37. Finish the solution to the vibrating circular membrane bywriting out a similar full solution.7. A copper cube 10.0 cm on a side is heated to 100° C. The block is placedon a surface that is kept at 0° C. The sides of the block are insulated, sothe normal derivatives on the sides are zero. Heat flows from the top ofthe block to the air governed by the gradient uz = -10°C/m. Determinethe temperature of the block at its center after 1.o minutes. Note that thethermal diffusivity is given by kis the density, and cp is the specific heat capacity.Kwhere K is the thermal conductivity,pCp'8. Consider a spherical balloon of radius a. Small deformations on thesurface can produce waves on the balloon's surface.a. Write the wave equation in spherical polar coordinates. (Note: p isconstant!)b. Carry out a separation of variables and find the product solutions forthis problem.c. Describe the nodal curves for the first six modes.

Given data: 10cm cube is heated to 100oC. Normal derivatives on the sides are zero, since the block sides are insulated. thermal diffusivity,k=Kρcp We need to calculate the temperature of the block at its center after 1.0minHeat flows gradually from block to air, In steady state, rate of heat flow remains constant. dQdt=KA∆Ql=constant∆Ql=constant100-010cm=100-θ5cm100 = 200-2θ2θ=100⇒θ=50°C

Answered: A copper cube 10.0 cm on a side is…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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Question

Number 7

6. We presented the full solution of the vibrating rectangular membrane
in Equation 6.37. Finish the solution to the vibrating circular membrane by
writing out a similar full solution.
7. A copper cube 10.0 cm on a side is heated to 100° C. The block is placed
on a surface that is kept at 0° C. The sides of the block are insulated, so
the normal derivatives on the sides are zero. Heat flows from the top of
the block to the air governed by the gradient uz = -10°C/m. Determine
the temperature of the block at its center after 1.o minutes. Note that the
thermal diffusivity is given by k
is the density, and cp is the specific heat capacity.
K
where K is the thermal conductivity,
pCp'
8. Consider a spherical balloon of radius a. Small deformations on the
surface can produce waves on the balloon's surface.
a. Write the wave equation in spherical polar coordinates. (Note: p is
constant!)
b. Carry out a separation of variables and find the product solutions for
this problem.
c. Describe the nodal curves for the first six modes.

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