Answer:
We can use the formula:
q = mcΔT
where q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
The heat transferred from the gold bar to the water is equal to the heat transferred from the water to the gold bar, since they reach thermal equilibrium. Therefore:
q_gold = q_water
We can solve for the temperature change of the gold bar:
q_gold = mcΔT_gold
q_water = mcΔT_water
Since the heat transferred is equal:
mcΔT_gold = mcΔT_water
Rearranging and solving for ΔT_gold:
ΔT_gold = ΔT_water(m_water/m_gold)
ΔT_water is the temperature change of the water, which is 17°C. m_water is 0.220 kg, and m_gold is 3 kg. c_gold is given as 129 J/kg K.
ΔT_gold = 17°C(0.220 kg/3 kg)(1/129 J/kg K) = 0.025°C
Therefore, the temperature change of the gold bar is 0.025°C when it is placed into 0.220 kg of water and thermal equilibrium is reached.