A metal block of mass 11.5 g gives off 360 J of heat while cooling from 99.7 to 32.5 oC. What is the specific heat of the metal in J g-1 oC-1?
To find the specific heat of the metal, we can use the equation:
Q = m * c * ΔT
Where:
Q is the amount of heat transferred (in joules)
m is the mass of the metal (in grams)
c is the specific heat of the metal (in J g^(-1) oC^(-1))
ΔT is the change in temperature (in oC)
In this case, we are given:
Q = 360 J
m = 11.5 g
ΔT = (32.5 - 99.7) oC
Substituting these values into the equation, we can solve for c:
360 J = 11.5 g * c * (32.5 - 99.7) oC
First, let's calculate the change in temperature:
ΔT = 32.5 - 99.7 = -67.2 oC
Now, we can rearrange the equation to solve for c:
360 J = 11.5 g * c * (-67.2 oC)
c = 360 J / (11.5 g * -67.2 oC)
c ≈ -0.50 J g^(-1) oC^(-1)
The specific heat of the metal is approximately -0.50 J g^(-1) oC^(-1).
To find the specific heat of the metal, we can use the formula:
Q = mcΔT
Where:
Q = heat energy (in Joules)
m = mass of the metal (in grams)
c = specific heat capacity of the metal (in J g^(-1) °C^(-1))
ΔT = change in temperature (in °C)
In this case, we are given:
Q = 360 J
m = 11.5 g
ΔT = (final temperature - initial temperature) = (32.5 °C - 99.7 °C)
Let's substitute the given values into the formula and solve for c:
360 J = (11.5 g)(c)(32.5 °C - 99.7 °C)
First, calculate the difference in temperature:
ΔT = (32.5 °C - 99.7 °C) = -67.2 °C
Now, substitute the values into the formula:
360 J = (11.5 g)(c)(-67.2 °C)
To isolate c, divide both sides of the equation by (11.5 g)(-67.2 °C):
c = 360 J / (11.5 g)(-67.2 °C)
Calculating this expression will give us the specific heat of the metal in J g^(-1) °C^(-1).