How much energy in kilojoules is needed to heat 5.00 g of ice from -10.0 C to 30.0 C ?
To calculate the amount of energy required to heat a substance, you can use the formula:
q = m * C * ΔT
Where:
q is the energy (in joules)
m is the mass of the substance (in grams)
C is the specific heat capacity of the substance (in joules per gram per degree Celsius)
ΔT is the change in temperature (in degrees Celsius)
First, we need to determine the mass of the ice in kilograms since the specific heat capacity is commonly given in joules per gram per degree Celsius. To convert grams to kilograms, divide the mass by 1000:
mass = 5.00 g / 1000 = 0.005 kg
Next, we need to find the specific heat capacity of ice. The specific heat capacity of ice is approximately 2.09 joules per gram per degree Celsius.
Now we can calculate the energy required using the formula:
q = m * C * ΔT
q = 0.005 kg * 2.09 J/g°C * (30.0°C - (-10.0°C))
Simplifying the equation:
q = 0.005 kg * 2.09 J/g°C * 40.0°C
q ≈ 0.418 J
To convert the energy from joules to kilojoules, divide the value by 1000:
q ≈ 0.418 J / 1000 = 0.000418 kJ
Therefore, the amount of energy needed to heat 5.00 g of ice from -10.0°C to 30.0°C is approximately 0.000418 kilojoules.
To calculate the energy required to heat a substance, you can use the formula:
Q = mcΔT
Where:
Q is the energy (in joules)
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance (in joules per gram per degree Celsius)
ΔT is the change in temperature (in degrees Celsius)
First, let's calculate the energy required to heat the ice from its initial temperature to its melting point (0°C).
Q1 = mcΔT1
m = 5.00 g
c = 2.09 J/g°C (specific heat capacity of ice)
ΔT1 = 0°C -(-10.0°C ) = 10.0°C
Q1 = (5.00 g)(2.09 J/g°C)(10.0°C)
Q1 = 104.5 J
Next, let's calculate the energy required to melt the ice.
Q2 = mL
m = 5.00 g
L = 333 J/g (latent heat of fusion for water)
Q2 = (5.00 g)(333 J/g)
Q2 = 1665 J
Now, let's calculate the energy required to heat the melted ice (water) from its melting point (0°C) to the final temperature (30°C).
Q3 = mcΔT3
m = 5.00 g
c = 4.18 J/g°C (specific heat capacity of water)
ΔT3 = 30.0 - 0 = 30.0°C
Q3 = (5.00 g)(4.18 J/g°C)(30.0°C)
Q3 = 627 J
Finally, add up all the energies to get the total energy required:
Total energy = Q1 + Q2 + Q3 = 104.5 J + 1665 J + 627 J
To convert this total energy to kilojoules, divide by 1000:
Total energy in kilojoules = (104.5 J + 1665 J + 627 J) / 1000
Total energy in kilojoules = 2.396 kJ
Therefore, approximately 2.40 kJ of energy is needed to heat 5.00 g of ice from -10.0°C to 30.0°C.