Graphite is frequently used in high-temperature applications because of its ability…
PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
Graphite is frequently used in high-temperature applications because of its ability to withstand extreme conditions. A research engineer needs to raise the temperature of a 250. g block of graphite from –35.0 °C to 230.0 °C. The graphite is heated inside an evacuated chamber so that no energy is exchanged with the surroundings other than that supplied by an electric resistance heater.
The specific heat capacity of graphite is temperature-dependent and can be approximated as
c(T)=0.612+1.15×10−4T where c is in Jg−1K−1 and T is in kelvins over the range 240 K ≤ T ≤ 570 K.
(a) Derive an integral expression for the total quantity of heat required to raise the temperature of the graphite block from its initial to its final temperature using the temperature-dependent form of c(T) provided.
(b) Evaluate the integral obtained in part (a) to determine the energy required, reporting your answer in kilojoules with three significant figures.
(c) The engineer has a power supply that can deliver a constant 150 W of electrical power. Calculate the minimum time, in minutes, necessary to supply the energy calculated in part (b), assuming 100 % conversion of electrical work to thermal energy within the graphite.
(d) Discuss one practical factor not considered in the calculation that could cause the actual heating time to be longer than the time predicted in part (c).