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?
answered above.
To determine the amount of heat required to raise the temperature of the metal from 35°C to 53°C, we can use the formula:
Q = mcΔT
Where:
Q is the heat transferred
m is the mass of the object (which cancels out with the next equation since it's constant)
c is the specific heat capacity of the metal
ΔT is the change in temperature (final temperature - initial temperature)
In this case, we are assuming the mass of the metal remains constant. Therefore, we can ignore the mass (m) term and focus on calculating the heat transfer (Q) using:
Q = cΔT
Given that 7.60 kJ of heat is needed to raise the temperature of the metal from 10°C to 25°C, we can use this information to find the specific heat capacity (c) of the metal.
Q = cΔT
7.60 kJ = c(25°C - 10°C)
Simplifying the equation:
7.60 kJ = 15c
c = (7.60 kJ) / 15
c = 0.5067 kJ/°C
Now that we have the specific heat capacity (c), we can use it to find the amount of heat required to raise the temperature of the metal from 35°C to 53°C.
Q = cΔT
Q = (0.5067 kJ/°C)(53°C - 35°C)
Q = (0.5067 kJ/°C)(18°C)
Q ≈ 9.122 kJ
Therefore, approximately 9.122 kJ of heat will be required to raise the temperature of the same sample of metal from 35°C to 53°C.