A 1.00 kg gold bar at 1010 K is dropped into 0.750 kg of sand at 25 °C. Assuming no heat is lost to the atmosphere, what is the final temperature of the sand?
To find the final temperature of the sand, we can use the principle of conservation of energy. The heat lost by the gold bar is equal to the heat gained by the sand.
The equation used for heat transfer is:
Q = m * c * ΔT
where:
Q is the heat transferred,
m is the mass of the substance,
c is the specific heat capacity of the substance, and
ΔT is the change in temperature.
First, let's find the heat lost by the gold bar:
Q_lost = m_gold * c_gold * ΔT_gold
Given:
m_gold = 1.00 kg (mass of gold bar)
c_gold = specific heat capacity of gold (consult a reference)
ΔT_gold = final temperature of gold bar - initial temperature of gold bar
Next, let's find the heat gained by the sand:
Q_gained = m_sand * c_sand * ΔT_sand
Given:
m_sand = 0.750 kg (mass of sand)
c_sand = specific heat capacity of sand (consult a reference)
ΔT_sand = final temperature of sand - initial temperature of sand
Since there is no heat lost to the atmosphere, the heat lost by the gold bar will equal the heat gained by the sand:
Q_lost = Q_gained
m_gold * c_gold * ΔT_gold = m_sand * c_sand * ΔT_sand
Rearranging the equation to solve for the final temperature of the sand:
ΔT_sand = (m_gold * c_gold * ΔT_gold) / (m_sand * c_sand)
Substituting the given values, we can calculate the final temperature of the sand.