1. On a scorching summer day a thirsty student finds a 500ml bottle of lemonade in the boot of the car. She measures the temperature of the lemonade to be 32 degrees Celsius. How much ice does she need to add to cool her lemonade down to a refreshing 4.0 degrees Celsius?
2. Calculate the final temperature of the salt water (specific heat capacity:3.5x10^3 J Kg^-1 K^-1) when all the water in the ice cream (specific heat capacity: 3.80 x 10^3J Kg^-1 K^-1)is frozen, assuming no other heat loss.
1. To figure out how much ice the student needs to add to cool her lemonade down, we can use the equation for heat transfer:
Q = mcΔT
Where Q is the heat transferred, m is the mass of the substance (in this case, the lemonade and ice), c is the specific heat capacity of the substance, and ΔT is the change in temperature.
Let's break down the steps to solve the problem:
Step 1: Calculate the heat transferred when the lemonade goes from 32 degrees Celsius to 4.0 degrees Celsius.
Q1 = m1 * c1 * ΔT1
= m1 * c_water * ΔT1
Here, m1 is the mass of the lemonade, c1 is the specific heat capacity of water, and ΔT1 is the change in temperature.
Step 2: Calculate the heat transferred when the ice goes from its initial temperature to 0 degrees Celsius.
Q2 = m2 * c2 * ΔT2
= m2 * c_ice * ΔT2
Here, m2 is the mass of the ice, c2 is the specific heat capacity of ice, and ΔT2 is the change in temperature.
Step 3: Calculate the heat transferred when the ice melts at 0 degrees Celsius.
Q3 = m2 * L
Here, L is the latent heat of fusion, which represents the heat required to change the state of a substance from solid to liquid without changing its temperature.
Step 4: Set up the equation to find the unknown mass of ice, m2.
Q1 + Q2 + Q3 = 0
Step 5: Substitute the known values into the equation and solve for m2.
Q1 + Q2 + Q3 = 0
m1 * c_water * ΔT1 + m2 * c_ice * ΔT2 + m2 * L = 0
Once you have solved for m2, you will know the mass of ice the student needs to add to cool her lemonade down to a refreshing 4.0 degrees Celsius.
2. To calculate the final temperature of the saltwater when all the water in the ice cream is frozen, we can use the principle of conservation of energy.
Q1 = Q2
Where Q1 is the heat transferred from the saltwater and Q2 is the heat transferred to the ice cream.
Let's break down the steps to solve the problem:
Step 1: Calculate the heat transferred from the saltwater.
Q1 = m1 * c1 * ΔT1
Here, m1 is the mass of the saltwater, c1 is the specific heat capacity of the saltwater, and ΔT1 is the change in temperature.
Step 2: Calculate the heat transferred to the ice cream.
Q2 = m2 * c2 * ΔT2 + m2 * L
Here, m2 is the mass of the ice cream, c2 is the specific heat capacity of the ice cream, ΔT2 is the change in temperature, and L is the latent heat of fusion.
Step 3: Set up the equation to find the final temperature of the saltwater, ΔT1.
Q1 = Q2
m1 * c_saltwater * ΔT1 = m2 * c_icecream * ΔT2 + m2 * L
Step 4: Substitute the known values into the equation and solve for ΔT1.
m1 * c_saltwater * ΔT1 = m2 * c_icecream * ΔT2 + m2 * L
Once you have solved for ΔT1, you can add it to the initial temperature of the saltwater to find the final temperature.