A hot, just minted copper coin is placed in 112g of water to cool. The water temperature changes by 8.58 C and the temperature of the coin changes by 80.0 C. What is the mass of the coin? Disregard any energy trans to the waters surroundings and assume the specific heat of copper is 387 j/kg C. The heat of water is 4186 J/kg C. Answer in units of g.
To find the mass of the coin, we can use the principle of heat transfer, which states that the heat gained or lost by a substance is given by the equation:
Q = mcΔT,
where Q is the heat transfer, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
In this case, we have two substances involved: water and copper. We need to consider the heat transfer for each substance separately.
For the water, the equation becomes:
Q_water = m_water * c_water * ΔT_water
For the copper coin, the equation becomes:
Q_copper = m_copper * c_copper * ΔT_copper
Since the heat gained by the water equals the heat lost by the coin, we can set up an equation:
Q_water + Q_copper = 0
m_water * c_water * ΔT_water + m_copper * c_copper * ΔT_copper = 0
Substituting the given values, we have:
112g * 4186 J/kg C * 8.58 C + m_copper * 387 J/kg C * (-80.0 C) = 0
Simplifying the equation gives us:
479383.04 + m_copper * (-30960) = 0
m_copper * (-30960) = -479383.04
m_copper = (-479383.04) / (-30960)
m_copper ≈ 15.5g
Therefore, the mass of the copper coin is approximately 15.5 grams.