The specific heat of granite is 0.80 kJ/kg*Celsius. If 1.6 MJ of heat are added to a 100-kg granite of statue of James Prescott Joule that is origanlly at 18 degrees Celsius, what is the final temperture of the statue?
To calculate the final temperature of the granite statue, we can use the equation:
Q = m * c * ΔT
Where:
Q is the heat added (in joules),
m is the mass of the granite (in kilograms),
c is the specific heat of granite (in kJ/kg*Celsius), and
ΔT is the change in temperature (in Celsius).
In this case, we have:
Q = 1.6 MJ = 1.6 * 10^6 kJ
m = 100 kg
c = 0.80 kJ/kg*Celsius
ΔT = ?
Rearranging the equation, we can solve for ΔT:
ΔT = Q / (m * c)
ΔT = (1.6 * 10^6 kJ) / (100 kg * 0.80 kJ/kg*Celsius)
ΔT = (1.6 * 10^6 kJ) / 80 kJ*Celsius
ΔT = 20,000 Celsius
To find the final temperature, we add the change in temperature to the initial temperature:
Final temperature = Initial temperature + ΔT
Final temperature = 18 Celsius + 20,000 Celsius
Final temperature = 20,018 Celsius
Therefore, the final temperature of the granite statue will be 20,018 degrees Celsius.
To find the final temperature of the statue, we can use the formula for heat transfer:
Q = mcΔT
Where:
Q is the heat transferred
m is the mass of the object
c is the specific heat capacity of the material
ΔT is the change in temperature
First, we need to convert the mass to kilograms:
100 kg = 100,000 grams
Next, we can substitute the values into the formula:
1.6 MJ = (100,000 g) * (0.80 kJ/kg*C) * ΔT
Converting the units to match (1 MJ = 1,000 kJ):
1.6 * 10^6 kJ = (100,000 g) * (0.80 kJ/kg*C) * ΔT
Simplifying:
ΔT = (1.6 * 10^6 kJ) / (100,000 g) * (0.80 kJ/kg*C)
ΔT = 16 * 10^4 / 8 * 10^1 * ΔT
ΔT = 20 C
Finally, we can calculate the final temperature:
Final temperature = Initial temperature + ΔT
Final temperature = 18 C + 20 C
Final temperature = 38 Celsius
Therefore, the final temperature of the statue will be 38 degrees Celsius.