Question #8e674

1 Answer
Jan 30, 2017

(I) Kinetic energy #KE=1/2mv^2#,
where #m# is mass of object and #v# its velocity.

Kinetic energy of Allegheny class locomotive is given by, where given velocity has been converted to SI units
#KE=1/2(5.368xx10^5)(72.0xx10^3/3600)^2#
#=>KE=1.0736xx10^8J#
(II) Converting to CGS units,
#KE=1.0736xx10^8/4.184cal#
#=>2.568421xx10^7cal# .....(1)
Since it is steam engine as such we need to consider heat lost by
(1) steam at #100^@C# to become water at #100^@C#
(2) water for #DeltaT=75.0^@C#

Let #m# be water needed to provide required heat.
Heat lost in step (1) #Q_1=mL#
where #L=539calcdotg^-1# is latent heat of vaporization of water
#=>Q_1=539m" "cal#

Heat lost in step (2) #Q_2=msDeltaT#
where #s=1calcdotg^-1cdotK^-1# is specific heat of water.
#=>Q_2=mxx1xx75.0#
#=>Q_2=75.0m#
Total heat lost #=Q_1+Q_2=539m+75.0m=614m" "cal# .....(2)

Assuming that there is no loss of heat and all lost heat is converted in the kinetic energy, equating (1) and (2)
#614m=2.568421xx10^7#
#=>m=(2.568421xx10^7)/614#
#=>m=4.183xx10^4g#