A 992.0-g iron meteor impacts the earth at a speed of 1447.0 m/s. If its energy is entirely converted to heat of the meteorite, what will the resultant temperature rise be? (The specific heat for iron is 113 cal/kg.C)
To calculate the resultant temperature rise, we can use the formula:
Q = mcΔT
Where:
Q = heat energy (in joules)
m = mass of the meteorite (in kilograms)
c = specific heat capacity of iron (in J/kg·°C)
ΔT = temperature change (in °C)
First, let's convert the mass from grams to kilograms:
Mass of the meteorite = 992.0 g = 0.992 kg
Next, we need to calculate the heat energy (Q) using the kinetic energy formula:
K.E. = 0.5mv^2
Where:
m = mass of the meteorite (in kilograms)
v = velocity of the meteorite (in meters per second)
K.E. = 0.5 * (0.992 kg) * (1447.0 m/s)^2
Now, let's plug in the values and calculate the kinetic energy.
K.E. = 0.5 * 0.992 * (1447.0)^2
Once we have the kinetic energy (Q), we can solve for the temperature change (ΔT) using the equation:
Q = mcΔT
ΔT = Q / (mc)
Now, let's plug in the values and calculate the temperature change.
ΔT = (K.E.) / (mc)
Finally, calculate the temperature change (ΔT) to find the resultant temperature rise for the meteorite.