PROBLEMS

2.1. A nonconducting container filled with 25kg of water at 20℃ is fitted with a stirrer, which is made to turn by gravity acting on weight of mass 35kg. The weight falls slowly through a distance of 5m in driving the stirrer. Assuming that all work done on the weight is transferred to the water and that the local acceleration of gravity is 9.8ms-2, determine:

(a) The amount of work on the water.

W=m∙∆z∙g=35[kg]∙5[m]∙9.8[m∙s^(-2)]=1715[J]

(b) The internal-energy change of the water.

U=Q+W

Q=0

∵This is insulated process.

U=W

U=1715[J]

(c) The final temperature of the water, for which C_p=4.18[kJ〖∙kg〗^(-1)∙℃^(-1)].

∆U=m∆TC_p

∆T=∆U/(m∙C_p )

∆T=(1715[J]∙(1[kJ])/(1000[J]))/(25[kg]∙4.18[kJ〖∙kg〗^(-1)∙℃^(-1)].)

∆T≅0.016[℃]

T_f=T_i+∆T

T_f=20[℃]+0.016[℃]

T_f=20.016[℃]

(d) The amount of heat that must be removed from the water to return it to its initial temperature.

Q=-∆U

Q= -1715[J]

(e) The total energy change of the universe because of (1) the process of lowering the weight, (2) the process of cooling the water back to its initial temperature, and (3) both processes together.

This process is reversible.

So reversed process don^' t loss the energy.

∆U_t=0