A silver block, initially at 59.8 ∘C, is submerged into 100.0 g of water at 24.6 ∘C, in an insulated container. The final temperature of the mixture upon reaching thermal equilibrium is 26.6 ∘C.
What is the mass of the silver block?
heat lost by silver = heat gained by water
heat change = mass * specific heat * temperature change
Σq = q(Ag) + q(H₂O) = (mcΔT)Ag + (mcΔT)H₂O = 0
=> m(Ag)(0.240j/g∙ᵒC)(26.6-59.8)ᵒC + (100g)(4.184(0.240j/g∙ᵒC)(26.6-24.6)ᵒC = 0
=> m(Ag)(-7.968j/g) + (836.8j) = 0
=> m(Ag) = (836.8/7.968)g = 105.2g
To find the mass of the silver block, we can use the principle of heat transfer, also known as the law of thermal equilibrium.
The equation used to solve this problem is:
(m1 * c1 * ΔT1) + (m2 * c2 * ΔT2) = 0
Where:
m1 = mass of the silver block
c1 = specific heat capacity of silver
ΔT1 = change in temperature of the silver block (final temperature - initial temperature)
m2 = mass of water
c2 = specific heat capacity of water
ΔT2 = change in temperature of the water (final temperature - initial temperature)
Given values:
m2 (mass of water) = 100.0 g
c2 (specific heat capacity of water) = 4.18 J/g·°C (approximate value for water)
ΔT2 (change in temperature of water) = 26.6 °C - 24.6 °C = 2.0 °C
To find the specific heat capacity of silver (c1), we need to refer to a table or reliable source. The specific heat capacity of silver is approximately 0.235 J/g·°C.
Now, let's plug the values into the equation:
(m1 * c1 * ΔT1) + (m2 * c2 * ΔT2) = 0
(m1 * 0.235 * ΔT1) + (100.0 * 4.18 * 2.0) = 0
Rearrange the equation to solve for m1:
(m1 * 0.235 * ΔT1) = - (100.0 * 4.18 * 2.0)
(m1 * ΔT1) = - (100.0 * 4.18 * 2.0) / 0.235
m1 * ΔT1 = - 3553.19
Since the final temperature of the mixture upon reaching thermal equilibrium is 26.6 °C (ΔT1 = 26.6 °C - 59.8 °C = -33.2 °C), we can now substitute this value:
m1 * -33.2 = -3553.19
m1 = -3553.19 / -33.2
m1 ≈ 107.05 g
Therefore, the mass of the silver block is approximately 107.05 grams.