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?
7600 joules = mass metal x specific heat x 15.
1). You can set up a ratio or
2) call mass metal x specific heat = k, evaluate k from the data in the first two lines. That is
(7600/15) = k, then
q = k*(53-35) and solve for q.
To find the amount of heat required to raise the temperature of the metal from 35°C to 53°C, we can use the concept of specific heat capacity.
The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of a unit mass of the substance by one degree Celsius (or one Kelvin).
To solve this problem, we need to make use of the equation:
Q = mcΔT
where Q represents the heat energy, m represents the mass of the substance, c represents the specific heat capacity, and ΔT represents the change in temperature.
Since the mass of the metal sample is not provided, we can assume that it remains constant. Therefore, we can ignore the mass in our calculation.
We are given that 7.60 kJ (kilojoules) of heat is needed to raise the temperature of the metal sample from 10°C to 25°C.
So, ΔT1 = (25°C - 10°C) = 15°C and Q1 = 7.60 kJ.
Now, we need to find Q2, the amount of heat required to raise the temperature of the same metal sample from 35°C to 53°C.
ΔT2 = (53°C - 35°C) = 18°C
To find Q2, we need to use the same specific heat capacity as in the first scenario, assuming it is constant for this metal sample.
Therefore, we can set up the following proportion:
Q1 / ΔT1 = Q2 / ΔT2
Substituting the given values:
7.60 kJ / 15°C = Q2 / 18°C
Now, we can solve for Q2:
Q2 = (7.60 kJ / 15°C) * 18°C
Q2 ≈ 9.12 kJ
So, approximately 9.12 kilojoules of heat will be required to raise the temperature of the same sample of metal from 35°C to 53°C.