we have an unknown mass of water at an initial temp of 35 degrees C and 100 g ice cube at -5 degrees, the final temp is 5 degrees. What is the mass of the water?
Specific heat of ice is 2100 j/(kg*k)
latent heat of fusion of ice is 333.7 kj/kg
To find the mass of water, we need to determine the amount of heat transferred between the water and ice.
First, let's calculate the heat transfer while raising the temperature of the water from 35°C to 5°C:
Q1 = (mass of water) x (specific heat of water) x (change in temperature of water)
Since we don't know the mass of the water, let's assign it a variable, say 'm'.
Q1 = m x specific heat of water x (final temperature - initial temperature)
Q1 = m x 4186 J/(kg·K) x (5°C - 35°C)
Q1 = -30m x 4186 J/kg
Next, we'll calculate the heat transfer during the melting of the ice:
Q2 = (mass of ice) x (latent heat of fusion)
The mass of the ice is given as 100 g or 0.1 kg.
Q2 = 0.1 kg x 333.7 kJ/kg
Q2 = 33.37 kJ = 33.37 × 10^3 J
Since heat is conserved, the total heat gained by the water is equal to the heat lost by the ice:
Q1 = Q2
Applying this equation, we can solve for the mass of water (m):
-30m x 4186 J/kg = 33.37 × 10^3 J
-30m = 33.37 × 10^3 J / 4186 J/kg
m = (33.37 × 10^3 J / 4186 J/kg) / -30
m ≈ -0.25 kg
The negative sign indicates that the water has lost mass during this process. However, mass cannot be negative, so it suggests that there might have been a mistake in the given information or calculations.
Please verify the values provided and try again.