Four 2cm×2cm×2cm cubes of ice are taken out from a refrigerator and are put in 200 ml of a drink at 10∘C.(a) Find the temperature of the drink when thermal equilibrium is attained in it.(b) If the ice cubs do not do not melt completely, find the amount melted. Assume that no heat is lost to the outside of the capacity. Density of ice =900kg/m3, density of the drink =1000kg/m3, specific heat capacity of the drink 4200 J/kg-K, latent heat of fusion of ice 3.4×105J/kg.

Question

Four 2cm×2cm×2cm cubes of ice are taken out from a refrigerator and are put in 200 ml of a drink at 10∘C.(a) Find the temperature of the drink when thermal equilibrium is attained in it.(b) If the ice cubs do not do  not melt completely, find the amount melted. Assume that no heat is lost to the outside of the capacity. Density of ice =900kg/m3, density of the drink =1000kg/m3, specific heat capacity of the drink 4200 J/kg-K, latent heat of fusion of ice 3.4×105J/kg.

Filo · Accepted Answer

Given:-Number of ice cube =4Volume of each ice cube=2×2×2=8cm2Density of ice=900kg/m3 Total number of ice, m1​=4×8×10−6×900=288×10−4kg​(a)Latent heat of fusion of ice,Li​=3.4×105J/kgDensity of the drink=1000kg/m3Volume of the drink=200mlmass of the drink=(200×10−6)∝1000kgLet first check the heat released when temperature of 200ml chargesfrom 10C to 0CHw​=(200×10−6×1000×4200×(10−0)=8400JHeat required to change four 8cm3 ice cube into water(Hi​)=mi​Li​=(288×10−4)×(3.4×105)=9792J∴ the heat required for melting the four cube of the iceis greater than the heat released by water.(Hi​>Hw​), some icewill remain solid and there will be equilibrium between ice and water.(b) Equilibrium temperature of the cube and the drink =0CLet M be the mass of the melted ice Hw​=(200×10−6×1000×4200×(10−0)=8400J∴M×(3.4×105)=8400J∴M=0.0247kg=25g

Question Text	Four $2 c m \times 2 c m \times 2 c m$ cubes of ice are taken out from a refrigerator and are put in 200 ml of a drink at $1 0^{\circ} C$ . (a) Find the temperature of the drink when thermal equilibrium is attained in it. (b) If the ice cubs do not do not melt completely, find the amount melted. Assume that no heat is lost to the outside of the capacity. Density of ice $= 900 k g / m^{3}$ , density of the drink $= 1000 k g / m^{3}$ , specific heat capacity of the drink 4200 J/kg-K, latent heat of fusion of ice $3.4 \times 1 0^{5} J / k g .$
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