how much heat would be required to warm Earths ocean by 1.0 degrees C assuming that the volume is 137*10^7 km ^3 and the density of sea water is 1.03 g/cm 3. also assume that the heat capacity of seawater is the same as that of water
To calculate the amount of heat required to warm Earth's ocean by 1.0 degree Celsius, we need to use the formula:
Q = mcΔT
where:
Q = amount of heat energy (in joules)
m = mass of the water (in kilograms)
c = specific heat capacity of water (in joules per kilogram per degree Celsius)
ΔT = change in temperature (in degrees Celsius)
First, let's find the mass of the water:
Volume of water (V) = 137 * 10^7 km^3
To convert cubic kilometers to cubic centimeters, we need to multiply by 10^15:
V = 137 * 10^22 cm^3
Density of seawater (ρ) = 1.03 g/cm^3
Mass (m) = Volume * Density:
m = V * ρ
m = (137 * 10^22 cm^3) * (1.03 g/cm^3)
m = 141.11 * 10^22 g
Next, we need to convert the mass from grams to kilograms:
m = 141.11 * 10^19 kg
Now, let's find the specific heat capacity of water:
The specific heat capacity of water (c) is approximately 4.184 J/g°C.
To convert grams to kilograms, we need to divide by 1000:
c = 4.184 J/(g°C) / 1000
c = 0.004184 J/(kg°C)
Finally, we can calculate the amount of heat energy required:
ΔT = 1.0 °C
Q = m * c * ΔT
Q = (141.11 * 10^19 kg) * (0.004184 J/(kg°C)) * (1.0 °C)
Now, let's calculate:
Q = 590.45 * 10^19 J
So, the amount of heat energy required to warm Earth's ocean by 1.0 degree Celsius is approximately 5.9045 * 10^21 Joules.
To calculate the amount of heat required to warm Earth's ocean by 1.0 degrees Celsius, we will use the formula:
Q = mcΔT
Where:
Q is the heat energy
m is the mass
c is the specific heat capacity
ΔT is the change in temperature
First, we need to calculate the mass of the ocean water.
Given:
Volume of seawater = 137 * 10^7 km^3
Density of seawater = 1.03 g/cm^3
To convert the volume to cubic centimeters (cm^3), we need to multiply it by (10^5 cm/km)^3:
Volume = 137 * 10^7 km^3 * (10^5 cm/km)^3 = 137 * 10^7 * (10^5)^3 cm^3
Now we can calculate the mass using the formula:
mass = volume * density
mass = 137 * 10^7 * (10^5)^3 cm^3 * 1.03 g/cm^3
Next, we need to convert the mass from grams to kilograms by dividing by 1000:
mass = 137 * 10^7 * (10^5)^3 cm^3 * 1.03 g/cm^3 / 1000 = (137 * 10^7 * 10^5 * 10^5 * 1.03) kg
Now, we can calculate the heat energy required using the specific heat capacity of water (c = 4.18 J/g°C):
Q = mass * c * ΔT
Q = (137 * 10^7 * 10^5 * 10^5 * 1.03) kg * 4.18 J/g°C * 1.0°C
Now we can simplify the expression:
Q = (137 * 10^7 * 10^5 * 10^5 * 1.03 * 4.18) kg * J/g
Q = 598.4 * 10^18 J
So, the amount of heat required to warm Earth's ocean by 1.0 degrees Celsius is approximately 598.4 * 10^18 Joules.