a) Two 36 g ice cubes are dropped into 300 g of water in a thermally insulated container. If the water is initially at 19°C, and the ice comes directly from a freezer at -19°C, what is the final temperature at thermal equilibrium? (b) What is the final temperature if only one ice cube is used? The specific heat of water is 4186 J/kg·K. The specific heat of ice is 2220 J/kg·K. The latent heat of fusion is 333 kJ/kg.
kindly tell me the ans for part a and b its an mcq and i am unable to solve it
To find the final temperature in each scenario, we need to consider the heat transfer that occurs between the water and the ice. Here's how you can solve part a and part b:
a) Two ice cubes are used:
Step 1: Calculate the heat gained or lost by the ice cubes:
First, calculate the heat lost by the ice cubes. Since the ice is coming directly from a freezer at -19°C, it needs to be heated to 0°C before it can start melting. The heat lost by the ice cubes can be calculated using the formula:
Q_ice = mass_ice * specific_heat_ice * (final_temperature_ice - initial_temperature_ice)
Q_ice = 2 * (36 g) * (2220 J/kg·K) * (0°C - (-19°C))
Next, calculate the heat gained by the ice cubes as they melt. Each ice cube will require a certain amount of heat to convert it from solid ice at 0°C to liquid water at 0°C. The heat gained by the ice cubes can be calculated using the formula:
Q_fusion = mass_ice * latent_heat_of_fusion
Q_fusion = 2 * (36 g) * (333 kJ/kg)
Step 2: Calculate the heat gained or lost by the water:
Next, calculate the heat gained by the water. The heat gained by the water can be calculated using the formula:
Q_water = mass_water * specific_heat_water * (final_temperature_water - initial_temperature_water)
Q_water = (300 g) * (4186 J/kg·K) * (final_temperature_water - 19°C)
Step 3: Set up the equation for heat transfer at thermal equilibrium:
At thermal equilibrium, the heat lost by the ice should be equal to the heat gained by the water. So we can set up the equation:
Q_ice + Q_fusion = Q_water
Step 4: Solve the equation for the final temperature:
Substitute the calculated values into the equation and solve for the final temperature.
b) One ice cube is used:
The process for finding the final temperature with one ice cube is the same as part a, except you only need to consider the heat transfer involving one ice cube. Repeat steps 1 to 4 for this scenario.
Once you have the equations, calculate the final temperature in both scenarios and compare them to find the correct answer for the multiple-choice question.