Heat - Energy Transfer Question

[Ve3Mike]

Hi, one of my homework problems i received was "A water heater can generate 32, 000kJ/h. How much water can it heat from 15 C to 50 C per hour?" I am having trouble figuring out what formula I would use?

 

[Chi Meson]

Let's see, you have the amount of heat, Q=32,000,000 J
you have a change in temperature, $$\Delta T$$=35 degrees
you have water with a specific heat, c = (look it up)
and you need mass m=?

You can't find the right formula? You should look again.

 

[quicknote]

Hi there,

To answer this question, you will need to use the formula for calculating heat transfer, which is Q = mcΔT, where Q is the heat transferred, m is the mass of the object, c is the specific heat capacity, and ΔT is the change in temperature.

In this case, since we are dealing with water, we can use the specific heat capacity of water, which is 4.186 J/g°C. We also know that the heat generated by the water heater is 32,000 kJ/h.

So, we can rearrange the formula to solve for the mass of water (m), which will give us the amount of water that can be heated by the water heater in one hour.

m = Q / (cΔT)

Substituting the values, we get:

m = (32,000,000 J/h) / (4.186 J/g°C * (50°C - 15°C))

m = 1,923,076.92 g = 1,923.08 kg

Therefore, the water heater can heat 1,923.08 kg of water from 15°C to 50°C in one hour.

I hope this helps! Let me know if you have any further questions.