What volume of 15 degree celsius water must be added to a 1.2KG piece of stainless steel at 85 degree celsius so that the final temperature is 35 degree celsius. assume the container in which the mixing takes place is perfectly insulated.
[mass H2O x specific heat H2O x (Tfinal-Tinitial)] + [mass steel x specific heat steel x (Tfinal-Tinitial)] = 0
mass H2O is the only unknown, solve for that.
To solve this problem, we can use the principle of heat transfer and the formula for heat gained or lost by a substance. The formula is:
Q = mcΔT
where Q is the heat gained or lost, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
First, let's calculate the heat lost by the stainless steel. Since it goes from 85°C to 35°C, the change in temperature (ΔT) is:
ΔT = 35°C - 85°C = -50°C
The specific heat capacity of stainless steel is approximately 500 J/kg°C, so the heat lost by the stainless steel can be calculated as:
Q_steel = m_steel * c_steel * ΔT
Given that the mass of the stainless steel is 1.2 kg and c_steel is 500 J/kg°C, we have:
Q_steel = 1.2 kg * 500 J/kg°C * (-50°C)
Next, let's calculate the heat gained by the water. Since it goes from 15°C to 35°C, the change in temperature (ΔT) is:
ΔT = 35°C - 15°C = 20°C
The specific heat capacity of water is 4186 J/kg°C, so the heat gained by the water can be calculated as:
Q_water = m_water * c_water * ΔT
We need to find the mass of the water (m_water) that gives us the same amount of heat gained as the steel lost:
Q_water = Q_steel
m_water * c_water * ΔT = Q_steel
Substituting the known values:
m_water * 4186 J/kg°C * 20°C = Q_steel
Now we can solve for the mass of water (m_water):
m_water = Q_steel / (4186 J/kg°C * 20°C)
Finally, we can calculate the volume of the water using the density of water (approximately 1000 kg/m³):
volume_water = m_water / density_water
Given that the density of water is 1000 kg/m³, we have:
volume_water = (Q_steel / (4186 J/kg°C * 20°C)) / 1000 kg/m³
By substituting the values and calculating, we can find the volume of water required to reach the desired final temperature.