Question #77a01

1 Answer
Nov 20, 2017

#\DeltaU = a(T_f^4 - T_i^4).V#
# = ( 7.566\times10^{-16} J/(m^3K^4))##\times(2.608\times10^{12} K^4)##\times(1 m^3)#
#= 197.3\times10^{-3}# #J = 197.3# #mJ#

Explanation:

Energy Density in radiation: #u = 4/c\sigmaT^4 = aT^4#,
#c=2.9979\times10^8# #m.s^{-1}# : Speed of light,
#\sigma = 5.670\times10^{-8}# #W/(m^2.K^4)# : Stefan-Boltzman Constant,
#a = 4/c\sigma = 7.566\times10^{-16}# #J/(m^3K^4)#

Total energy in cavity radiation is : #U = u.V#
Change in total energy in cavity radiation is : #\Delta U = \Delta u.V#

#\Delta U = a(T_f^4-T_i^4).V#

Given:
#T_i = 100^oC + 273.15 = 373.15# #K#
#T_f = 1000^oC + 273.15 = 1273.15# #K#
#V = 1000# #L = 1# #m^3#.

#\DeltaU = a(T_f^4 - T_i^4).V#
# = ( 7.566\times10^{-16} J/(m^3K^4))##\times(2.608\times10^{12} K^4)##\times(1 m^3)#
#= 197.3\times10^{-3}# #J = 197.3# #mJ#