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 is

Options

A. `(10)/(7)kg`
B. `(5)/(7)kg`
C. `(5)/(4)kg`
D. `(5)/(8)kg`

Answer

B

Explanation

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`