How long does it take an immersion heater with a 500 W power rating to heat up 500 g of h2o from 15 c to 100 c if the water is in an aluminum cup with mass 200 g. the specific heat of aluminum is 99 j/ (kg K)
So you must heat 500 g H2O from 15 C to 100 C + 200 g Al dish from 15 C to 100 C.
q for H2O = 500 x 4.184 J/g x (100-15) = ? joules
q for Al dish = 200 x 0.099 J/g x (100-15) = ? joules
total q = qH2O + qAl = ? joules
The heater is 500 watts which is 500 Joule/second
500 J/s x # seconds = ? total J from above. Solve for seconds. Post your work if you get stuck.
To calculate the time it takes for an immersion heater to heat up water, we can use the equation:
Q = mcΔT
Where:
Q is the heat energy required to raise the temperature of the water.
m is the mass of the water.
c is the specific heat of water.
ΔT is the change in temperature.
First, let's calculate the heat energy required to heat up the water:
Q = mcΔT
Q = (500g + 200g) × 99 J/(kg·K) × (100°C - 15°C)
Q = 700g × 99 J/(kg·K) × 85°C
Next, we'll convert the mass to kilograms:
m = 700g ÷ 1000
m = 0.7kg
Substituting the values into the equation:
Q = (0.7kg) × (99 J/(kg·K)) × (85°C)
Now, we need to calculate the time it takes using power and energy:
Power = Energy / Time
Since we know the power rating of the heater is 500W, we can rearrange the formula and solve for time:
Time = Energy / Power
Time = Q / Power
Calculating the time:
Time = (0.7kg × 99 J/(kg·K) × 85°C) / 500W
By calculating the expression on the right-hand side, we can get the time in seconds.