A copper vessel of mass 1000gm contains 500 gm of water at 50 degrees Celsius. A

Question

A copper vessel of mass 1000gm contains 500 gm of water at 50 degrees Celsius. An ice cube of mass 100 gm at temperature -30 degrees Celsius is dropped into this vessel. Does the ice melt? What is the final temperature ? Repeat part b, if at the same time as dropping in the ice cube, we also drop in a 200 gm glass at a temperature of 110 degrees Celsius A copper vessel of mass 1000gm contains 500 gm of water at 50 degrees Celsius. An ice cube of mass 100 gm at temperature -30 degrees Celsius is dropped into this vessel. Does the ice melt? What is the final temperature ? Repeat part b, if at the same time as dropping in the ice cube, we also drop in a 200 gm glass at a temperature of 110 degrees Celsius Does the ice melt? What is the final temperature ? Repeat part b, if at the same time as dropping in the ice cube, we also drop in a 200 gm glass at a temperature of 110 degrees Celsius

Explanation / Answer

Let Specific heat capacity of ice=2030Jkg-1K-1 ; CCuooper =386 Jkg-1K-1 ; Cwater=4200 ; Latent heat of fusion=336000

Total heat to be absorbed to melt the whole ice cube(Q1)= 0.1*[(2030*30)+336000]=39690 J------(1)

Total heat rejected from copper and water(Q2)= 50[0.5*4200 + 286]=124300 J ------(2)

Since (2) is greater than (1) ; it is possible to melt the ice.

Assume whole ice cube is melted and final temperature is T; From conservation of energy [temperature difference for copper and 50C water is= 50-T]

Q1+(4200*0.1*T)= (50-T)*[0.5*4200 + 386] ;

T=29.116 0C ;

Take Cglass=840Jkg-1K-1 ; As above calculation

Q1+(4200*0.1*T) = (50-T)*[0.5*4200 + 386] +(0.2*840*(110-T)) ;

T=33.536 0C

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