A cooking vessel on a slow burner contains 5 kg of water and an unknown mass of ice in equilibrium at `0^@C` at time `t=0`. The temperature of the mixture is measured at various times and the result is plotted as shown in Fig. During the first 50 min the mixture remains at `0^@C`. From 50 min to 60 min, the temperature increases to `2^@C` Neglecting the heat capacity of the vessel, the initial mass of the ice isA. `(10)/(7)kg`B. `(5)/(7)kg`C. `(5)/(4)kg`D. `(5)/(8)kg`

A cooking vessel on a slow burner contains 5 kg of water and an unkno

1.	A cooking vessel on a slow burner contains 5 kg of water and an unknown mass of ice in equilibrium at `0^@C` at time `t=0`. The temperature of the mixture is measured at various times and the result is plotted as shown in Fig. During the first 50 min the mixture remains at `0^@C`. From 50 min to 60 min, the temperature increases to `2^@C` Neglecting the heat capacity of the vessel, the initial mass of the ice isA. `(10)/(7)kg`B. `(5)/(7)kg`C. `(5)/(4)kg`D. `(5)/(8)kg`
Answer» Correct Answer - B Let m be the mass of ice. Rate of heat given by the burner is constant. In the first 50 min `(dQ)/(dt)=(mL)/(t_1)=(mkgxx(80xx4.2xx10^3)J//kg)/((50min))` .(i) From 50 min to 60 min `(dQ)/(dt)=((m+5)S_(H_2O)Deltatheta)/(t_2)` `=((m+5)kg(4.2xx10^3)J//kg xx2^@C)/(10min)` ..(ii) From Eqs. (i) and (ii) `(80m)/(50)=(2(m+5))/(10)` `7m=5impliesm=(5)/(7)kg=0.7kg`

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