If 72.4 kJ of heat is supplied to a 752 g block of metal, the temperature of the metal increases by 9.95°C. Calculate the specific heat capacity of the metal in J/g·°C.
I cannot find the information in my textbook, and I don't understand the equation needed to do the work on the summer assignment...
q = mc*delta T
q = heat = 72,400J
m = 752g
c = specific heat = ?
dT = 9.95
Solve for c.
q = mcdT
72 400 = 752 X C X 9.95
C = 9.676 J/C
To calculate the specific heat capacity of the metal, you can use the equation:
Q = mcΔT
Where:
Q = heat energy supplied to the metal (in Joules)
m = mass of the metal (in grams)
c = specific heat capacity of the metal (in J/g·°C)
ΔT = change in temperature of the metal (in °C)
Plugging the given values into the equation, we have:
72.4 kJ = (752 g) * c * (9.95°C)
First, convert the heat energy from kJ to J:
72.4 kJ = 72.4 * 1000 J = 72400 J
Now, rearrange the equation to solve for the specific heat capacity:
c = (Q) / (m * ΔT)
c = (72400 J) / (752 g * 9.95°C)
c ≈ 9.67 J/g·°C
Therefore, the specific heat capacity of the metal is approximately 9.67 J/g·°C.
To calculate the specific heat capacity of the metal, you need to use the equation:
q = m * c * ΔT
where:
- q is the heat supplied to the metal (in joules, J),
- m is the mass of the metal (in grams, g),
- c is the specific heat capacity of the metal (in J/g·°C), and
- ΔT is the change in temperature of the metal (in °C).
In this problem, you are given:
- q = 72.4 kJ = 72,400 J (since 1 kJ = 1,000 J)
- m = 752 g
- ΔT = 9.95 °C
Now, let's solve for c:
Rearranging the equation, we have:
c = q / (m * ΔT)
Substituting the given values:
c = 72,400 J / (752 g * 9.95 °C)
To get the specific heat capacity in J/g·°C, divide the heat supplied by the product of the mass and change in temperature.
Let's do the math:
c ≈ 9.63 J/g·°C
Therefore, the specific heat capacity of the metal is approximately 9.63 J/g·°C.