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A rod is initially at a uniform temperature of 0°C
Chapter 17, Problem 112P(choose chapter or problem)
A rod is initially at a uniform temperature of 0°C throughout. One end is kept at 0°C, and the other is brought into contact with a steam bath at 100°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 cm2, its length is 120 cm, its thermal conductivity is 380 W/m · K, its density is 1.00 × 104 kg/m3, and its specific heat is 520 J/kg · K. Consider a short cylindrical element of the rod 1.00 cm in length. (a) If the temperature gradient at the cooler end of this element is 140 C°/m, how many joules of heat energy flow across this end per second? (b) If the average temperature of the element is increasing at the rate of what is the temperature gradient at the other end of the element?
Questions & Answers
QUESTION:
A rod is initially at a uniform temperature of 0°C throughout. One end is kept at 0°C, and the other is brought into contact with a steam bath at 100°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 cm2, its length is 120 cm, its thermal conductivity is 380 W/m · K, its density is 1.00 × 104 kg/m3, and its specific heat is 520 J/kg · K. Consider a short cylindrical element of the rod 1.00 cm in length. (a) If the temperature gradient at the cooler end of this element is 140 C°/m, how many joules of heat energy flow across this end per second? (b) If the average temperature of the element is increasing at the rate of what is the temperature gradient at the other end of the element?
ANSWER:Solution 112P Step 1: In this question, we need to find how many joules of heat energy flows across the rod per second The rate at which temperature gradient flows from one end to other