How Long to Heat 250g of Water with a 250-Watt Heater?

[wakejosh]

Homework Statement

its a long story problem so ill break it down:
an electric heater generates 250 Watts of electricity, how long will it take for 250 grams of water to heat from 20 C to 80 C

The Attempt at a Solution

so 80 C - 20 C = 60 C , i have to heat it 60 C
250 grams of water X 60 C = 15000 Calories
4.184 X 15000 = 62760 Joules

62760 J / 250 watts = 251 seconds / 60 = 4.18 min

so it will take 4.18 min. Is this correct?

 

[berkeman]

I didn't check the math, but it looks like your approach is correct.

 

[kyle8921]

I would like to provide a more detailed explanation for the solution to this problem. The first step is to convert the temperature change from Celsius to Kelvin, as the unit of energy (Joules) is based on the Kelvin scale. So, 80 C is equal to 353.15 K and 20 C is equal to 293.15 K. The temperature change is then 353.15 K - 293.15 K = 60 K.

Next, we need to calculate the amount of energy required to heat 250 grams of water by 60 K. This can be done using the specific heat capacity of water, which is 4.184 J/g*K. So, the energy required is 250 grams x 60 K x 4.184 J/g*K = 62760 J.

Now, we can use the formula Power = Energy/Time to calculate the time it will take to heat the water. Rearranging the formula, we get Time = Energy/Power. Plugging in the values, we get Time = 62760 J/250 watts = 251 seconds.

Finally, we convert the time from seconds to minutes by dividing by 60, giving us a total time of 4.18 minutes. Therefore, it will take approximately 4.18 minutes for an electric heater generating 250 watts to heat 250 grams of water from 20 C to 80 C.