please homework help

A bowl of 582 g of water is placed in a microwave oven that puts out 729 watts (J/s). How long would it take in seconds to increase the temperature of the water from 12.0oC to 46.6oC?

q = mass H2O x specific heat H2O x (Tfinal-Tinitial)

729 J/s x #seconds = q
Solve for # seconds.

To calculate the time it takes to increase the temperature of the water, we need to use the formula:

Q = mcΔT

Where:
Q is the heat energy absorbed by the water,
m is the mass of the water,
c is the specific heat capacity of water, and
ΔT is the change in temperature.

First, let's calculate the heat energy absorbed by the water using the formula:

Q = mcΔT

The specific heat capacity of water, c, is approximately 4.18 J/g°C.

Given that the mass of the water, m, is 582 g and the change in temperature, ΔT, is (46.6 - 12.0) = 34.6°C.

Plugging the values into the formula, we get:

Q = (582 g) * (4.18 J/g°C) * (34.6°C)

Now, let's calculate the time it takes to increase the temperature of the water using the formula:

Q = Pt

Where:
Q is the heat energy absorbed by the water (calculated earlier),
P is the power of the microwave oven, and
t is the time in seconds.

Given that the power of the microwave oven, P, is 729 watts (J/s), let's solve for t:

Q = Pt

Substituting the value of Q calculated earlier, we have:

(582 g) * (4.18 J/g°C) * (34.6°C) = (729 watts) * t

Now, solve for t:

t = (582 g * 4.18 J/g°C * 34.6°C) / 729 watts

Plugging the values into the equation and calculating, we get:

t = (87438.612 J) / 729 watts

t ≈ 120 seconds

Therefore, it would take approximately 120 seconds for the water to increase its temperature from 12.0°C to 46.6°C in the microwave oven.