Please i cannot find any help on this question so far

[bharp24]

please... i cannot find any help on this question so far!

A rod is initially at a uniform temperature of 0 degress celsius throughout. One end is kept at 0 degress celsius, and the other is brought into contact with a steam bath at 100degrees celsius. The surface of the rod is insulated so that heat can flow only lengthwise along the rod. The cross-sectional area of the rod is 2.50 cm^2 , its length is 120 cm, its thermal conductivity is 380 W/m * K, its density is 1.00 x 10^4 kg/m^3, and its specific heat capacity is 520 J/ kg * K. Consider a short cylindrical element of the rod 1.00 cm in length.

1.If the temperature gradient at the cooler end of this element is 140 deg C/m, how many joules of heat energy flow across this end per second?

2.If the average temperature of the element is increasing at the rate of 0.250 deg C/sec, what is the temperature gradient at the other end of the element?

I have gotten number 1 to be 13.3W and know it is correct, but really need help on number 2.

I have been trying to find what the average temperature gradient even is and am not successful. If anyone knows anything about how to do this problem, your posts would be greatly apprecitated!

 

[jbsteele]

Answer to Question 2: The average temperature gradient of the element is equal to the rate of change of temperature with respect to length, or in this case, 0.250 deg C/sec. Therefore, the temperature gradient at the other end of the element is also 0.250 deg C/sec.

 

[Moetasim]

I understand your frustration in not being able to find help on this question so far. Let me try to assist you with the second part of the question.

To find the temperature gradient at the other end of the element, we can use the heat conduction equation:

Q/t = -kA(dT/dx)

Where:
Q/t is the rate of heat flow (in joules per second)
k is the thermal conductivity of the rod
A is the cross-sectional area of the rod
dT/dx is the temperature gradient
x is the distance along the rod

We know that the rate of heat flow at the cooler end is 13.3 W (as you calculated in the first part of the question). We also know that the length of the element is 1 cm. Substituting these values into the equation, we get:

13.3 W = - (380 W/m*K)(2.50 cm^2)(dT/dx)

Solving for dT/dx, we get:

dT/dx = -0.021 deg C/cm

This means that for every 1 cm increase in length along the rod, there is a decrease of 0.021 deg C in temperature. We can use this value to find the temperature gradient at the other end of the element.

Since the length of the rod is 120 cm, the temperature gradient at the other end can be calculated as:

dT/dx = (0.021 deg C/cm)(120 cm) = 2.52 deg C

Therefore, the temperature gradient at the other end of the element is 2.52 deg C per 1 cm. I hope this helps you with the second part of the question. If you have any further questions, please feel free to ask.