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

**1. Homework Statement**

A rod is initially at a uniform temperature of 0 ^deg C throughout. One end is kept at 0 ^deg C, and the other is brought into contact with a steam bath at 100 ^deg C. 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?

**2. Homework Equations**

**3. The Attempt at a Solution**

I have gotten number 1 to be 13.3W, but do not know how to proceed with number 2. Any help would be greatly appreciated!