Question #187540

A piece of ice of mass mice = 80g, which is initially at -15℃ is dropped into an isolated container with negligible heat capacity. The container contains 150g of water at 80℃. Determine the final temperature of the system? 


(Ci = 2093 J/kg℃, Cw = 4186 J/kg℃, Lf = 333 KJ/kg)


1
Expert's answer
2021-05-03T10:31:16-0400

Heat require to reach to temperature of ice at 0oc0 ^oc

Q=msΔTQ= m s\Delta T

=0.080×2093×(15)=0.080\times 2093\times (15)

=2511.6J=2511.6J

Heat require to melt the ice

Q1=mLQ_1=mL

=0.080×333000J=0.080\times 333000 J

=26640J=26640J

Hence, total energy require to melt the ice =Q+Q1=Q+Q_1

=26640+2511.6=26640+2511.6

=29151.6J=29151.6J

Thermal energy of 150g of water at 8080^\circ

=0.150×4200×80J=0.150\times 4200\times 80J

=50400J=50400J

Hence we can say that ice will get melt completely.

29151.6J=0.08×4200(t)+0.15×4200×(80t)\Rightarrow 29151.6J=0.08\times 4200(t)+0.15\times 4200 \times (80-t)

336t+50400630t=29151.6J\Rightarrow 336t+50400-630t=29151.6J

294t=21248.4J\Rightarrow 294t=21248.4J


t=21248.4294\Rightarrow t=\frac{21248.4}{294}^\circ

t=72,27C\Rightarrow t= 72,27^\circ C


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