A 455-g chunk of iron is removed from an oven and plunged into 385g water in an insulated container. The temperature of the water increases from 27 degrees celsius to 89 degrees celsius.

If the specific heat of iron is 0.449 J g^-1 degrees Celsius^-1, what must have been the original temperature of the iron?

See your post above.

[massFe x specific heatFe x (Tfinal-Tinitial)] + [mass water x specific heat water x (Tfinal-Tinitial)] = 0

To find the original temperature of the iron, we can use the principle of conservation of energy. The heat gained by the water is equal to the heat lost by the iron.

The heat gained by the water can be calculated using the formula:

Q_water = m_water * c_water * ΔT_water

Where:
Q_water is the heat gained by the water
m_water is the mass of the water (385g)
c_water is the specific heat capacity of water (4.184 J g^-1 degrees Celsius^-1)
ΔT_water is the change in temperature of the water (89°C - 27°C = 62°C)

So, Q_water = (385g) * (4.184 J g^-1 degrees Celsius^-1) * (62°C)

The heat lost by the iron is equal to the heat gained by the water, so:

Q_iron = -Q_water

To find Q_iron, we can use the formula:

Q_iron = m_iron * c_iron * ΔT_iron

Where:
Q_iron is the heat lost by the iron
m_iron is the mass of the iron (455g)
c_iron is the specific heat capacity of iron (0.449 J g^-1 degrees Celsius^-1)
ΔT_iron is the change in temperature of the iron (T_iron_initial - T_iron_final)

Substituting the known values, we have:

-Q_water = (455g) * (0.449 J g^-1 degrees Celsius^-1) * (T_iron_initial - T_iron_final)

Since we want to find the original temperature of the iron (T_iron_initial), we rearrange the equation:

T_iron_initial = (Q_water / (m_iron * c_iron)) + T_iron_final

Plugging in the known values, we get:

T_iron_initial = (Q_water / (455g * 0.449 J g^-1 degrees Celsius^-1)) + 89°C

Now, we can calculate T_iron_initial:

T_iron_initial = (Q_water / (455g * 0.449 J g^-1 degrees Celsius^-1)) + 89°C

By evaluating this expression, we can determine the original temperature of the iron.