If 7.60 kJ of heat is needed to raise the temperature of a sample of metal from 10.°C to 25°C, how many kilojoules of heat will be required to raise the temperature of the same sample of metal from 35°C to 53°C?
To calculate the amount of heat required to raise the temperature of a sample of metal, we need to use the heat capacity formula.
The formula to calculate heat is:
Q = m * c * ΔT
Where:
Q is the heat energy (in joules)
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance (in J/g·°C)
ΔT is the change in temperature (in °C)
In this case, we have the temperature change (ΔT) and the amount of heat required (Q) for the first scenario.
Given:
ΔT1 = 25°C - 10°C = 15°C
Q1 = 7.60 kJ = 7,600 J
We know that the ratio of heat to temperature change is constant, so we can use this ratio to find the heat required for the second scenario.
We can set up a proportion:
Q1 / ΔT1 = Q2 / ΔT2
Plugging in the known values:
7,600 J / 15°C = Q2 / (53°C - 35°C)
Simplifying the equation:
Q2 = (7,600 J / 15°C) * (18°C)
Calculating:
Q2 = 7,600 J * 18 / 15 = 9,120 J
Finally, converting the heat from joules to kilojoules:
Q2 = 9,120 J / 1,000 = 9.12 kJ
Therefore, 9.12 kilojoules of heat will be required to raise the temperature of the same sample of metal from 35°C to 53°C.