37.3k views
5 votes
A piece of metal with a specific heat capacity of 0.475 J/gºC at a temperature of 100.0°C is dropped into an

insulated container of water. The volume of water is 199.0 mL and its temperature before adding the metal is
22°C The final temperature of the water is 25°C. The specific heat capacity of water is 4.184 J/gºC. What is
the mass of the metal? q=mcAT

1 Answer

1 vote

Answer:

First, we need to calculate how much heat was lost by the metal as it cooled from 100°C to the final temperature (which we will assume is 25°C, since we are not given the exact temperature). The formula for calculating heat is:

q = mcΔT

where q is heat, m is mass, c is specific heat capacity, and ΔT is the change in temperature.

The metal lost heat in this process, so the value of q will be negative. We can rearrange the formula to solve for the mass of the metal:

m = q / (cΔT)

We are given the specific heat capacity of the metal (0.475 J/gºC), the initial temperature (100°C), and the final temperature (25°C). We also know that the heat lost by the metal (q) must be equal to the heat gained by the water. We can use the formula:

qmetal = -qwater

to relate the heat lost by the metal to the heat gained by the water. We know the specific heat capacity of water (4.184 J/gºC), the volume of water (199.0 mL, or 199.0 g), and the initial and final temperatures of the water (22°C and 25°C). We can use the formula:

qwater = mcΔT

to calculate the heat gained by the water. Plugging in the given values, we get:

qwater = (199.0 g)(4.184 J/gºC)(25°C - 22°C) = 2503.8 J

Therefore, the heat lost by the metal must be:

qmetal = -2503.8 J

Now we can use the formula for mass to calculate the mass of the metal:

m = q / (cΔT)

m = (-2503.8 J) / (0.475 J/gºC)(100°C - 25°C)

m = 35.6 g

Therefore, the mass of the metal is 35.6 g.

User Hung Vu
by
9.0k points