Question

A 4.6-kg block of ice originally at 263 K is placed in thermal contact with a 15.7-kg block of silver (cAg = 233 J/kg-K) which is initially at 1052 K. The H2O - silver system is insulated so no heat flows into or out of it.At what temperature will the system achieve equilibrium?

Answer 1

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 × $10^{5}$ 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 × $10^{5}$ + 4.6 × 4286 × ( T - 273 )

solve we get

T =  326.44 K

so temperature at  326.44 K system achieve equilibrium