A piece of a newly synthesized material of

mass 25.0 g at 80.0

C is placed in a calorimeter containing 100.0 g of water at 20.0

C. If
the final temperature of the system is 24.0

C,
what is the specific heat capacity of this material?

1.20

[mass material + specific heat material x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0

Solve for Tfinal.

To find the specific heat capacity of the material, we can use the following formula:

Q = mcΔT

Where:
Q = heat absorbed or lost by the material
m = mass of the material
c = specific heat capacity of the material
ΔT = change in temperature

In this case, the material is gaining heat from the water, so we can calculate the heat gained by the material using the formula:

Q = mcΔT

Since the water is losing heat, we can calculate the heat lost by the water using the same formula:

Q = mwCwΔT

Where:
mw = mass of the water
Cw = specific heat capacity of water
ΔT = change in temperature

Since no heat is exchanged with the surroundings, the heat gained by the material is equal to the heat lost by the water:

mcΔT = -mwCwΔT

Rearranging the equation to solve for c:

c = -(mwCwΔT) / (mΔT)

We are given the following values:
m = 25.0 g (mass of the material)
mw = 100.0 g (mass of the water)
Cw = 4.18 J/g°C (specific heat capacity of water)
ΔT = (24.0°C - 20.0°C) = 4.0°C (change in temperature)

Plugging in the values, we can calculate the specific heat capacity of the material:

c = -(100.0 g * 4.18 J/g°C * 4.0°C) / (25.0 g * 4.0°C)

c = -1672 J / 100 J

c ≈ -16.72 J/g°C

Note: The negative sign indicates that the material is losing heat.

To find the specific heat capacity of the material, we can use the principle of heat transfer, which states that the heat gained by one object is equal to the heat lost by another object in thermal contact.

First, let's determine the heat gained by the material:

Q(material) = m(material) * c(material) * ΔT
Where:
- Q(material) is the heat gained by the material (in Joules)
- m(material) is the mass of the material (in grams)
- c(material) is the specific heat capacity of the material (in J/g⋅°C)
- ΔT is the change in temperature of the material (final temperature - initial temperature)

Q(material) = 25.0 g * c(material) * (24.0°C - 80.0°C)

Now, let's determine the heat lost by the water:

Q(water) = m(water) * c(water) * ΔT
Where:
- Q(water) is the heat lost by the water (in Joules)
- m(water) is the mass of the water (in grams)
- c(water) is the specific heat capacity of water (4.18 J/g⋅°C, approximately)
- ΔT is the change in temperature of the water (final temperature - initial temperature)

Q(water) = 100.0 g * 4.18 J/g⋅°C * (24.0°C - 20.0°C)

According to the principle of heat transfer:
Q(material) = -Q(water) (since heat lost by water is gained by the material)

So, we can set up the equation:
25.0 g * c(material) * (24.0°C - 80.0°C) = -100.0 g * 4.18 J/g⋅°C * (24.0°C - 20.0°C)

Now, solve the equation for c(material):

c(material) = (-100.0 g * 4.18 J/g⋅°C * (24.0°C - 20.0°C)) / (25.0 g * (24.0°C - 80.0°C))

Evaluate the expression to find the value of c(material).