Question

A 108.7 g piece of copper (specific heat 0.380 j/g･°c) is heated and then placed into 400.0 g of water initially at 20.7°c. the water increases in temperature to a final temperature of 22.2°c. What is the initial temperature (in °c) of the copper?

Answer 1

The initial temperature of the copper is 22.6554°C.

Step-by-step explanation:

To find the initial temperature of the copper, we can use the formula for heat transfer: q = mcΔT, where q is the heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

First, let's find the heat transferred from the copper to the water:

The heat transferred from the copper to the water is equal to the heat gained by the water: qcopper = qwater.

1. Using the formula q = mcΔT, we can calculate the heat gained by the water: qwater = mcΔT.
2. Substituting the given values, we have: qcopper = (108.7g)(0.380J/g･°C)(Ti - 22.2°C).

We can assume that the heat transferred is conserved, so qcopper = qwater.

By equating the two expressions for the heat transferred, we can solve for the initial temperature of the copper, Ti:

(108.7g)(0.380J/g･°C)(Ti - 22.2°C) = (400.0g)(4.18J/g･°C)(22.2°C - 20.7°C).

Simplifying and solving for Ti, we get:

Ti - 22.2°C = (400.0g)(4.18J/g･°C)(22.2°C - 20.7°C) / (108.7g)(0.380J/g･°C)

Ti - 22.2°C = 0.4554°C

Ti = 22.2°C + 0.4554°C

Ti = 22.6554°C

Answer 2

To calculate the initial temperature of the copper, you can use the formula for heat transfer.

Step-by-step explanation:

To calculate the initial temperature of the copper, we can use the formula for heat transfer:

q = mCΔT

Where,

• q is the heat transfer,
• m is the mass of the substance,
• C is the specific heat capacity of the substance, and
• ΔT is the change in temperature.

For the copper, we have:

• m = 108.7 g
• C = 0.380 J/g∙°C
• ΔT = Final temperature of copper - Initial temperature of copper

For the water, we have:

• m = 400.0 g
• C = 4.18 J/g∙°C (specific heat capacity of water)
• ΔT = Final temperature of water - Initial temperature of water

Since the heat transfer between the copper and water is equal, we can set up an equation:

mCΔTcopper = mCΔTwater

Simplifying this equation, we get:

108.7 * 0.380 * (Final temperature of copper - Initial temperature of copper) = 400.0 * 4.18 * (Final temperature of water - 20.7)

Now, we can solve for the initial temperature of the copper.