**Answer:**

**temperature at 326.44 K system achieve equilibrium**

**Explanation:**

**given data **

mass of block of ice = 4.6 kg

temperature = 263 K

thermal contact = 15.7-kg

specific heat of silver cAg = 233 J/kg-K

initially temperature = 1052 K

**to find out **

what temperature will the system achieve equilibrium

**solution**

first we consider final temperature of the system is T

we know that specific heat of water (C w) = 4186 J(kg K)

and

specific heat of ice ( C i ) = 2030 J/(kg K)

and

latent heat of fusion of ice ( Lf ) = 3.33 × J/kg

and we know that system is insulated

so **heat lost by silver = heat generated by ice ** .................1

so we can say

mass of silver × specific heat of silver × ( initial temp - final temp ) = mass of ice × specific heat of ice × ( ice temp ) + mass of ice × latent heat of fusion of ice + mass of ice × specific heat of water × (final temperature )

put here value we get

mass of silver × specific heat of silver × ( initial temp - final temp ) = mass of ice × specific heat of ice × ( ice temp ) + mass of ice × latent heat of fusion of ice + mass of ice × specific heat of water × (final temperature )

15.7 × 233 × ( 1052 - T ) = 4.6 × 2030 × 10 + 4.6 × 3.33 × + 4.6 × 4286 × ( T - 273 )

solve we get

T = 326.44 K

**so temperature at 326.44 K system achieve equilibrium**