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.