Consider two identical iron nails: One nail is heated to 95 °C, the other is cooled to 15 °C. The two nails are placed in a coffee cup calorimeter and the system is allowed to come to thermal equilibrium. What is the final temperature of the two nails?

Is water in the calorimeter"? If not, then

mass Fe x sp.h.Fe x (Tf-95) + mass Fe x sp.h.Fe x (Tf-15) = 0
Tf = 55 if I did it right. Check my work. Since mass and sp.h. are the same, the easy way is to assign arbitrary numbers to mass and sp.h. (I used 1 to make it easier).

To find the final temperature of the two nails when they reach thermal equilibrium, we can use the concept of heat transfer between objects.

The heat lost by the hot nail will be equal to the heat gained by the cold nail. This is based on the principle of conservation of energy.

The heat lost or gained by an object can be calculated using the formula:

Q = mcΔT

Where:
Q = heat energy
m = mass
c = specific heat capacity
ΔT = change in temperature

Since the two nails are identical, their masses and specific heat capacities are the same. Let's assume the mass and specific heat capacity of each nail to be 'm' and 'c', respectively.

So, the heat lost by the hot nail is Q1 = mc(95 °C - Tf), and the heat gained by the cold nail is Q2 = mc(Tf - 15 °C), where Tf is the final temperature.

According to the law of conservation of energy, Q1 = Q2.

mc(95 °C - Tf) = mc(Tf - 15 °C)

Now let's solve for Tf:

95 °C - Tf = Tf - 15 °C

Adding Tf to both sides:

95 °C = 2Tf - 15 °C

Adding 15 °C to both sides:

110 °C = 2Tf

Dividing both sides by 2:

Tf = 55 °C

Therefore, the final temperature of the two nails when they reach thermal equilibrium is 55 °C.

To determine the final temperature of the two nails when they reach thermal equilibrium, we can make use of the principle of energy conservation.

The principle of energy conservation states that in an isolated system, the total energy remains constant. When the two nails are placed in the calorimeter, they will exchange heat until reaching equilibrium, and we can assume that no heat is lost to the surroundings.

To solve this problem, we can use the equation:

m1 * c * (Tf1 - T1) = -m2 * c * (Tf2 - T2)

Where:
m1 and m2 are the masses of the nails, which are identical, so we can consider them as the same value, let's say "m".
c is the specific heat capacity of iron.
Tf1 and Tf2 are the final temperatures of the two nails.
T1 and T2 are the initial temperatures of the two nails.

We know that the initial temperature of one nail is 95 °C (T1 = 95 °C), and the initial temperature of the other nail is 15 °C (T2 = 15 °C).

As the two nails are identical, they have the same mass, so we can consider m1 = m2 = m.

Now, we just need the specific heat capacity of iron, which is approximately 0.45 J/g°C.

Plugging in all the values into the equation, we can solve for Tf1 and Tf2:

m * 0.45 * (Tf1 - 95) = -m * 0.45 * (Tf2 - 15)

As the masses cancel out, we can simplify further:

0.45 * (Tf1 - 95) = -0.45 * (Tf2 - 15)

Dividing both sides by 0.45, we get:

Tf1 - 95 = -Tf2 + 15

Rearranging the equation, we have:

Tf1 + Tf2 = 110

Since the two nails reach thermal equilibrium, their final temperatures will be the same, so Tf1 = Tf2. We can substitute this into the equation:

2 * Tf1 = 110

Dividing both sides by 2, we find:

Tf1 = 55°C

Therefore, the final temperature of the two nails when they reach thermal equilibrium in the coffee cup calorimeter would be 55 °C.