To solve this problem, we can use the principle of conservation of energy.
First, we need to calculate the heat lost by the ice cube to cool down from -8.5°C to its melting point:
Q1 = m_ice * c_ice * (0°C - (-8.5°C))
Where:
Q1 = heat lost by the ice cube (in Joules)
m_ice = mass of the ice cube (unknown)
c_ice = specific heat capacity of ice (given as 2100 J/(kg°C))
Next, we need to calculate the heat lost by the ice cube to melt:
Q2 = m_ice * L
Where:
Q2 = heat lost by the ice cube to melt (in Joules)
L = latent heat of fusion of ice (given as 3.35 x 10^5 J/kg)
The total heat lost by the ice cube is the sum of Q1 and Q2:
Q_total = Q1 + Q2
Now, we need to calculate the heat gained by the water to increase its temperature from 20°C to 17°C:
Q_water = m_water * c_water * (17°C - 20°C)
Where:
Q_water = heat gained by the water (in Joules)
m_water = mass of the water (given as 310 g, or 0.31 kg)
c_water = specific heat capacity of water (given as 900 J/(kg°C))
According to the principle of conservation of energy, the heat lost by the ice cube is equal to the heat gained by the water:
Q_total = Q_water
Substituting the expressions for Q_total, Q1, Q2, and Q_water, we can solve for the unknown mass of the ice cube:
m_ice * c_ice * (0°C - (-8.5°C)) + m_ice * L = m_water * c_water * (17°C - 20°C)
m_ice * (c_ice * (0°C - (-8.5°C)) + L) = m_water * c_water * (17°C - 20°C)
m_ice = (m_water * c_water * (17°C - 20°C)) / (c_ice * (0°C - (-8.5°C)) + L)
Plugging in the given values:
m_ice = (0.31 kg * 900 J/(kg°C) * (17°C - 20°C)) / (2100 J/(kg°C) * (0°C - (-8.5°C)) + 3.35 x 10^5 J/kg)
Calculating this expression will give you the mass of the ice cube.
A cube of ice is taken from the freezer at -8.5°C and placed in a 15g aluminium calorimeter filled with 310g of water at room temperature of 20°C. The final temperature of water is observed to be 17°C What is the mass of the ice cube? 18] [Given cice 21001/kg C, CA 9001/kg°C, L-3.35 x 10 J/kgl
1 answer