The oven draws 1100W of power, and you have determined that it heats with an efficiency of 51%. Using this information, determine the time t it would take to bring 240mL of water from 25C to 100C . Note that 4.2 J of energy is required to raise the temperature of 1.0mL of water by 1.0C.
.51 * 1100 = 561 Watts = 561 Joule/second
561 t = heat in
= 240 mL * (75 deg C) (4.2 Joule/mLdegC)
so
t = 240*75*4.2/561
=135 seconds
about 2 minutes and 15 seconds
This must be a microwave oven.
To determine the time it would take to bring 240mL of water from 25°C to 100°C using an oven with a power of 1100W and an efficiency of 51%, we need to follow these steps:
Step 1: Calculate the total amount of energy required to heat the water.
The energy required to raise the temperature of water can be calculated using the formula:
Energy = (mass of water in grams) x (specific heat capacity of water) x (change in temperature)
In this case, we have the following values:
- Mass of water = 240mL = 240g (since the density of water is approximately 1g/mL)
- Specific heat capacity of water = 4.2 J/g·°C (as given)
- Change in temperature = (100°C - 25°C) = 75°C
Energy = (240g) x (4.2 J/g·°C) x (75°C)
Energy = 75,600 J
Step 2: Calculate the time required to heat the water using the oven's power and efficiency.
Power is the rate at which energy is transferred or used, and it is measured in watts (W). Efficiency represents the effectiveness of the oven in converting energy into useful work. It can be expressed as a decimal or a percentage.
Efficiency = 0.51 (or 51%)
Power = 1100W
Knowing that power is the rate of energy transfer (or work done) per unit time, we can use the formula:
Power = Energy / Time
Since we want to find the time, we can rearrange the equation:
Time = Energy / Power
Plugging in the values, we get:
Time = 75,600 J / 1100 W
Time ≈ 68.73 seconds
So, it would take approximately 68.73 seconds to bring 240mL of water from 25°C to 100°C using the given oven.
To determine the time it would take to bring 240mL of water from 25°C to 100°C using an oven with a power draw of 1100W and an efficiency of 51%, we need to calculate the amount of energy required and then divide it by the power.
Step 1: Calculate the energy required to heat the water:
Energy = mass × specific heat capacity × ΔT
Where:
- mass = 240 mL of water = 240 g (since the density of water is 1 g/mL)
- specific heat capacity of water = 4.2 J/g°C
- ΔT = change in temperature = final temperature - initial temperature = 100°C - 25°C = 75°C
Energy = 240 g × 4.2 J/g°C × 75°C
Energy = 75600 J
Step 2: Calculate the time t using the power and energy:
Efficiency = (useful output energy / input energy) × 100%
51% = (useful output energy / (1100W × t)) × 100%
Rearrange the equation:
(useful output energy / input energy) = 51% / 100%
(useful output energy) = (51% / 100%) × input energy
useful output energy = 0.51 × input energy
Therefore,
0.51 × input energy / (1100W × t) = 51% / 100%
0.51 × input energy = (51% / 100%) × (1100W × t)
0.51 × input energy = 0.51 × (1100W × t)
Now substitute the input energy with the calculated energy:
0.51 × 75600 J = 0.51 × (1100W × t)
Step 3: Solve for t:
0.51 × 75600 J = 0.51 × 1100W × t
38676 J = 561W × t
t = 38676 J / 561W
t ≈ 69 seconds
Therefore, it would take approximately 69 seconds to bring 240mL of water from 25°C to 100°C using the given oven.