A large container is separated into two halves by a 2.0 cm thick glass divider. The area of the divider is 0.25 m^2 and the thermal conductivity of glass is 0.90W/m•K. Each side is filled with 30 kg of water, specific heat 4180 J/kg•K, at different temperatures. Initially, the temperature difference is 20 K. How long will it take before the temperature difference is 1.0 K?

To solve this problem, we can use the formula for heat transfer:

Q = (kAΔT)t

Where:
- Q is the amount of heat transferred
- k is the thermal conductivity of the material (in this case, glass)
- A is the area of the glass divider
- ΔT is the temperature difference across the divider
- t is the time

In this case, we want to find the time it takes for the temperature difference to change from 20 K to 1.0 K.

First, let's calculate the initial heat transfer across the glass divider.

Q_initial = (0.90 W/m•K)(0.25 m^2)(20 K)

Next, let's determine the amount of heat transfer needed to decrease the temperature difference from 20 K to 1.0 K.

Q_final = (0.90 W/m•K)(0.25 m^2)(1.0 K)

The difference between the initial and final heat transfers will be equal to the heat transfer rate multiplied by the time.

Q_initial - Q_final = (0.90 W/m•K)(0.25 m^2)(20 K - 1.0 K)t

Simplifying further:

Q_initial - Q_final = (0.90 W/m•K)(0.25 m^2)(19 K)t

Now, rearranging the equation to solve for time:

t = (Q_initial - Q_final) / [(0.90 W/m•K)(0.25 m^2)(19 K)]

Let's plug in the values to find the time:

t = [(0.90 W/m•K)(0.25 m^2)(20 K) - (0.90 W/m•K)(0.25 m^2)(1.0 K)] / [(0.90 W/m•K)(0.25 m^2)(19 K)]

After simplification, we can find the value of t by dividing the numerator by the denominator.

t = (0.45 J) / (0.405 J/K)

t = 1.111 s

Therefore, it will take approximately 1.111 seconds for the temperature difference to decrease from 20 K to 1.0 K.

i don't know how to solve this question.