A 1000W heater is placed in an insulated beaker containing 750g of water at 100 ∘ C. The water vapour is allowed to escape. Assume that there is no loss to the surroundings via conduction, convection or radiation. The specific latent heat of vaporisation of water is 2260kJ/kg.Part AWater leftHow much water is left after 5.0minutes?

To solve this problem, we first need to understand that the heater is using its power to convert the water into steam. The amount of water that can be converted into steam depends on the power of the heater and the time it is left on.

Step 1: Convert power to energy The power of the heater is given in watts (W), which is a unit of power equivalent to one joule per second. To find the total energy used by the heater, we multiply the power by the time the heater is left on. However, the time is given in minutes, so we first need to convert it to seconds:

5 minutes = 5 * 60 = 300 seconds

Then we multiply the power of the heater by the time it is left on to find the total energy:

1000W * 300s = 300,000J

Step 2: Convert energy to mass The specific latent heat of vaporisation of water is the amount of energy needed to convert 1kg of water into steam without changing its temperature. It is given in kJ/kg, so we first need to convert it to J/kg:

2260kJ/kg = 2260 * 1000 = 2,260,000J/kg

Then we divide the total energy by the specific latent heat of vaporisation to find the mass of water that can be converted into steam:

300,000J / 2,260,000J/kg = 0.133kg

Step 3: Convert mass to volume The mass of water is given in grams, so we first need to convert it to kilograms:

750g = 0.75kg

Then we subtract the mass of water that can be converted into steam from the total mass of water to find the mass of water left:

0.75kg - 0.133kg = 0.617kg

So, after 5 minutes, there is 0.617kg or 617g of water left in the beaker.

To solve this problem, we first need to find out how much energy the heater can provide in 5 minutes.

Step 1: Convert the power of the heater to kilowatts. 1000W = 1kW

Step 2: Convert the time from minutes to seconds. 5 minutes = 300 seconds

Step 3: Calculate the total energy provided by the heater. Energy = Power x Time Energy = 1kW x 300s = 300kJ

Step 4: Calculate the amount of water that can be vaporized using this energy. The specific latent heat of vaporization of water is the amount of energy needed to change 1kg of water from liquid to gas without changing its temperature. In this case, it is given as 2260kJ/kg.

Amount of water vaporized = Energy / Specific latent heat of vaporization Amount of water vaporized = 300kJ / 2260kJ/kg = 0.133kg

Step 5: Convert the initial amount of water from grams to kilograms. 750g = 0.75kg

Step 6: Subtract the amount of water vaporized from the initial amount to find out how much water is left. Water left = Initial amount - Amount vaporized Water left = 0.75kg - 0.133kg = 0.617kg

So, after 5 minutes, there is 0.617kg of water left in the beaker.