400.0g of a metal absorbs 10000.J of heat energy and its temperature rises from 20.0*C to 103.0*C. What is he specific heat of the metal
.30 joule/gram-degree celsius
q = mass x specific heat x delta T.
To find the specific heat of the metal, we can first calculate the heat energy absorbed using the formula:
Q = m * c * ΔT
Where:
Q = heat energy absorbed (in Joules)
m = mass of the metal (in grams)
c = specific heat of the metal (in J/g°C)
ΔT = change in temperature (in °C)
Given:
Mass of the metal (m) = 400.0 g
Heat energy absorbed (Q) = 10000 J
Initial temperature (T1) = 20.0 °C
Final temperature (T2) = 103.0 °C
First, we calculate the change in temperature:
ΔT = T2 - T1
ΔT = 103.0 °C - 20.0 °C
ΔT = 83.0 °C
Next, we rearrange the formula to solve for the specific heat (c):
Q = m * c * ΔT
c = Q / (m * ΔT)
Substituting the given values into the formula:
c = 10000 J / (400.0 g * 83.0 °C)
Now, let's calculate the specific heat:
c = 10000 J / (33200 g °C)
And, simplifying the equation:
c ≈ 0.3012 J/g°C
Therefore, the specific heat of the metal is approximately 0.3012 J/g°C.
To find the specific heat of the metal, we can use the formula:
q = m * c * ΔT
Where:
- q is the heat energy absorbed by the metal,
- m is the mass of the metal,
- c is the specific heat capacity of the metal,
- ΔT is the change in temperature of the metal.
In this case, we know the following values:
- q = 10,000 J (heat energy absorbed)
- m = 400.0 g (mass of the metal)
- ΔT = (final temperature - initial temperature) = (103.0°C - 20.0°C)
So, plugging in the values into the formula, we can rearrange to solve for c:
c = q / (m * ΔT)
Now let's calculate the specific heat:
c = 10,000 J / (400.0 g * (103.0°C - 20.0°C))
c = 10,000 J / (400.0 g * 83.0°C)
c = 10,000 J / (33,200 g°C)
c ≈ 0.3012 J/g°C
Therefore, the specific heat of the metal is approximately 0.3012 J/g°C.