Answer:
d. 37°C
Explanation:
When Equilibrium is reached,
Heat lost = heat gain.
Heat lost by the hot metal = c₁m₁(T₁-T₂)............. equation 1
Where c₁ = specific heat capacity of the metal = 0.25 cal/g⋅°C, m₁ = mass of the metal = 250 g, T₁ = initial Temperature of the metal = 70°C, T₂ final temperature of the metal .
Substituting this values into equation 1,
Heat lost by the metal = 62.5(70-T₂)
Also,
Heat gain by the water = c₂m₂(T₂-T₁)................. equation 2
c₂ = 1.00 cal/g⋅°C., m₂ = 75 g, T₁ = 20°C
Substituting this values into equation 2,
Heat gain by water = 1× 75 (T₂ - 20)
Heat gained by water = 75(T₂ - 20)
Also,
Heat gained by the calorimeter = c₃m₃(T₂-T₁)............. equation 3
Where c₃ = 0.10 cal/ g⋅°C, m =500 g, T₁ =20°C.
Substituting this values into equation 3
Heat gained by the calorimeter = 0.1 × 500(T₂ - 20)
Heat gained by the calorimeter = 50(T₂ - 20)
Heat lost by the metal = heat gained by water + heat gained by the calorimeter.
62.5(70-T₂) = 50(T₂ - 20) + 75(T₂ - 20)
4375 - 62.5T₂ = 50T₂ - 1000 + 75T₂ - 1500
Collecting like terms,
-62.5T₂ - 50T₂ - 75T₂ = - 1000 - 1500 - 4375
-187.5T₂ = -6875
Dividing both side by the coefficient of T₂
-187.5T₂ / -187.5 = -6875 /-187.5
T₂ = 36.666°C
T₂ ≈ 37°C
The final temperature = 37°C
, so if we apply the previous formula we find the index of refraction of the medium: