To treat a burn on your hand, you decide to place an ice cube on the burned skin. The mass of the ice cube is 10.9 g, and its initial temperature is -12.0 °C. The water resulting from the melted ice reaches the temperature of your skin, 29.6 °C. How much heat is absorbed by the ice cube and resulting water?
q = [mass ice x specific heat solid ice x [0-(-12)] + [mass ice x heat fusion] + [mass melted ice x specific heat liquid H2O x (29.6-0)]
8376.42
To calculate the amount of heat absorbed by the ice cube and resulting water, we can use the equation:
Q = mcΔT
Where:
Q is the amount of heat absorbed,
m is the mass of the substance (in this case, the ice cube and resulting water),
c is the specific heat capacity of the substance, and
ΔT is the change in temperature.
First, we need to calculate the heat absorbed by the ice cube as it melts. To do this, we'll use the specific heat capacity of ice, which is 2.09 J/g·°C.
Q_ice = m_ice * c_ice * ΔT_ice
Where:
Q_ice is the amount of heat absorbed by the ice cube,
m_ice is the mass of the ice cube, and
ΔT_ice is the change in temperature of the ice cube.
Given:
m_ice = 10.9 g
c_ice = 2.09 J/g·°C
ΔT_ice = 0 °C - (-12.0 °C) = 12.0 °C
Plugging in the values, we have:
Q_ice = 10.9 g * 2.09 J/g·°C * 12.0 °C
By multiplying these values, we can determine the heat absorbed by the ice cube.
Next, we need to calculate the heat absorbed by the resulting water as it warms up. To do this, we'll use the specific heat capacity of water, which is 4.18 J/g·°C.
Q_water = m_water * c_water * ΔT_water
Where:
Q_water is the amount of heat absorbed by the water,
m_water is the mass of the water, and
ΔT_water is the change in temperature of the water.
To determine the mass of the water, we subtract the mass of the ice cube from the total mass of the ice cube and resulting water.
m_water = m_tot - m_ice
Given:
m_tot = 10.9 g
m_ice = 10.9 g
Using this information, we can calculate the mass of the water.
Finally, we substitute the values into the equation to calculate the heat absorbed by the water.
Q_water = m_water * c_water * ΔT_water
Once we have calculated both Q_ice and Q_water, we can add them together to find the total amount of heat absorbed by the ice cube and resulting water.