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Explanation / Answer

from the 1st law of thermodynamics,

W on system + Q = change in total energy of system

W on system + 0 = change in internal energy + change in kinetic energy + change in kinetic potential energy

or W on system + 0 = 0 + change in kinetic energy + m* g* ( h2-h1)

( heat given and change in internal energy are zero).

or, change in kinetic energy = W on system - m*g*(h2-h1) = 3210 Btu - (110 lb)*(32.17 ft/s^2) *(32800 ft-16400 ft)=3210 Btu - 58.0347 *10^6 lb-ft^2/s^2 = ( 3210 - (58.0347 * 10^6)/ 25037 ) Btu = 892.043 Btu

now change in kinetic energy = 1/2*m*(V2^2-V1^2)

or 892.043 Btu = 1/2 * (110 lb) * ( V2^2 - 164^2)

or 892.043 * 25037 = 1/2 * 110 * ( V2^2 - 164^2)

or solving above we get V = 658 ft/s

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