If an object is heated, the temperature of the object will increase. The thermal

Question

If an object is heated, the temperature of the object will increase. The thermal energy (Q) associated with a change in temperature (delta T) is a function of the mass of the object (m) and the specific heat (C_p). Specific heat is a material property, and values are available in literature. In an experiment, heat is applied to the end of an object, and the temperature change at the other end of the object is recorded. An unknown material is tested in the lab yielding the following results. (a) Show the resulting data and trendline, with equation and R^2 value on the appropriate graph type (xy scatter, semilog, or log-log) to make the data appear linear. (b) If the material was titanium, what mass of sample was tested? (c) If a 4-gram sample was used, which of the following materials was tested?

Explanation / Answer

the mass m = slope / log(e)

m = ( 1 decade / 80 - 20 ) / 0.43

m = 0.0387

considering the trendline equation C

y = b exp ( mx ) --- 1

now substituting the values

y = 1.5 exp ( 0.0387 x ) --- 2

then

C = 1.5 exp ( 0.0387 x )

now

m t = 1

m = 1/t

b = C / exp ( m t )

the values b is 1.5 g/cm3

the unit for m is 0.039 and 1/day

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