200 g of ice at 0ºC put in 500 g of water at 20C. The system is in a
container with negligible heat capacity and which is isolated from
surroundings.
a)What will be the final temperature (at equilibrium) of the system?
b)How much ice is melting?
Yes IM response
Responsibilities
To determine the final temperature of the system, you can use the principle of conservation of energy.
a) First, let's calculate the heat gained or lost by each substance. The heat gained or lost can be expressed using the formula:
Q = m * c * ΔT
Where:
Q is the heat gained or lost
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature
For water:
Q_water = m_water * c_water * ΔT_water
Given:
m_water = 500 g (mass of water)
c_water = 4.18 J/g·°C (specific heat capacity of water)
ΔT_water = final temperature - initial temperature = final temperature - 20°C
For ice:
Q_ice = m_ice * c_ice * ΔT_ice
Given:
m_ice = 200 g (mass of ice)
c_ice = 2.09 J/g·°C (specific heat capacity of ice)
ΔT_ice = final temperature - initial temperature = final temperature - 0°C
In this case, since the system is isolated, the heat gained by the water is equal to the heat lost by the ice:
Q_water = -Q_ice
Substituting the equations, we have:
m_water * c_water * ΔT_water = -m_ice * c_ice * ΔT_ice
Now, let's solve for the final temperature (ΔT_water and ΔT_ice will cancel out):
m_water * c_water * (final temperature - 20°C) = -m_ice * c_ice * final temperature
Next, let's substitute the given values:
500 g * 4.18 J/g·°C * (final temperature - 20°C) = -200 g * 2.09 J/g·°C * final temperature
Solving this equation will give you the final temperature of the system.
b) To determine how much ice is melting, you need to calculate the heat required to melt the ice using the formula:
Q_melt = m_ice * ΔH_melt
Where:
Q_melt is the heat required to melt the ice
m_ice is the mass of ice
ΔH_melt is the enthalpy of fusion or heat of fusion of ice, which is 334 J/g
Substituting the values:
Q_melt = 200 g * 334 J/g
Solving this equation will give you the amount of ice that melted in terms of energy.
Note: Don't forget to convert grams to kilograms (divide by 1000) and round the final answers to the appropriate significant figures.