A 1.8 kg piece of a metal initially at a temperature of 180oC is dropped into the water with mass of 14 kg. The water is in a container made of the same metal with mass 3.6 kg. The initial temperature of the water and container is 16.0oC, and the final temperature of the entire system (including the container) is 18.0oC. Calculate the specific heat of the metal.

Question

A 1.8 kg piece of a metal initially at a temperature of 180oC is dropped into the water with mass of 14 kg. The water is in a container made of the same metal with mass 3.6 kg. The initial temperature of the water and container is 16.0oC, and the final temperature of the entire system (including the container) is 18.0oC. Calculate the specific heat of the metal.

Answer 1

the sum of heats gained is zero.

Heatgainedwater+heatgainedmetal=0
14kg*cw*(18.0-16.0)+(1.8+3.6)kg*Cm*(18.0-180)=0
solve for cmetal cm

Answer 2

I need help I don't know how to solve it

Answer 3

To calculate the specific heat of the metal, we can use the principle of heat transfer:

1. Calculate the heat transferred to the water:
The heat transferred to the water can be calculated using the formula:
Q_water = mass_water * specific_heat_water * change_in_temperature

Given:
mass_water = 14 kg
specific_heat_water = 4.186 J/g°C (specific heat capacity of water)
change_in_temperature = (final temperature - initial temperature) = (18.0°C - 16.0°C) = 2.0°C

Converting mass_water to grams since the specific heat of water is given in J/g°C:
mass_water = 14 kg * 1000 g/kg = 14000 g

Plugging the values into the formula:
Q_water = 14000 g * 4.186 J/g°C * 2.0°C = 117304 J

2. Calculate the heat transferred to the container:
The heat transferred to the container can be calculated using the same formula as above:
Q_container = mass_container * specific_heat_container * change_in_temperature

Given:
mass_container = 3.6 kg
specific_heat_container = specific_heat_metal (since the container is made of the same metal)

Plugging the values into the formula:
Q_container = 3.6 kg * specific_heat_metal * 2.0°C

3. Calculate the heat transferred from the metal to the water and container:
The heat transferred from the metal can be calculated by subtracting the heat transferred to the water and container from the initial heat of the metal:
Q_metal = initial_heat_metal - (Q_water + Q_container)

The initial heat of the metal can be calculated using the formula:
initial_heat_metal = mass_metal * specific_heat_metal * change_in_temperature

Given:
mass_metal = 1.8 kg
specific_heat_metal = unknown

Plugging the values into the formula:
initial_heat_metal = 1.8 kg * specific_heat_metal * (180.0°C - 16.0°C)

4. Solve for the specific heat of the metal:
Rearranging the equation for Q_metal:
Q_metal = mass_metal * specific_heat_metal * change_in_temperature = initial_heat_metal - (Q_water + Q_container)

Substituting the values and solving for specific_heat_metal:
specific_heat_metal = (initial_heat_metal - Q_water - Q_container) / (mass_metal * change_in_temperature)

Answer 4

To calculate the specific heat of the metal, we need to use the principle of conservation of energy. The heat gained by the water and container is equal to the heat lost by the metal.

Let's denote the specific heat of the metal as C and the change in temperature as ΔT. The heat gained by the water and container is given by:

Q_water = (mass_water + mass_container) * specific_heat_water * ΔT_water

And the heat lost by the metal is given by:

Q_metal = mass_metal * specific_heat_metal * ΔT_metal

Since the final temperature is the same for both the metal and the water, we have:

ΔT_water = ΔT_metal

Now, we can set up the equation:

Q_metal = Q_water

mass_metal * specific_heat_metal * ΔT_metal = (mass_water + mass_container) * specific_heat_water * ΔT_water

Substituting the given values:

1.8 kg * C * ΔT_metal = (14 kg + 3.6 kg) * 4.186 J/g°C * (18.0°C - 16.0°C)

Simplifying the equation:

1.8 kg * C * ΔT_metal = 17.6 kg * 4.186 J/g°C * 2.0°C

1.8 kg * C * ΔT_metal = 147.44 J

Dividing both sides by ΔT_metal:

C = 147.44 J / (1.8 kg * ΔT_metal)

Now, we need to determine the value of ΔT_metal. We can use the equation:

ΔT_metal = final temperature - initial temperature

Substituting the given values:

ΔT_metal = 18.0°C - 180.0°C

ΔT_metal = -162.0°C

Note that the final temperature is given in Celsius, so we need to convert it to Kelvin by adding 273.15:

ΔT_metal = -162.0°C + 273.15

ΔT_metal = 111.15 K

Finally, substituting the values into the equation for C:

C = 147.44 J / (1.8 kg * 111.15 K)

C ≈ 0.892 J/g°C

Therefore, the specific heat of the metal is approximately 0.892 J/g°C.