- #1
FAS1998
- 50
- 1
Homework Statement
1.2.6. Supose that the specific heat is a function of position and temperature, c(x,u).
(a)Show that the heat energy per unit mass necesary to raise the temperature of a thin slice of thickness deltax from 0°to u(x,t) is not c(x)u(x,t), but instead int((0->u)c(x,u’))du’.
Homework Equations
The Attempt at a Solution
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I believe c(x,u) gives the energy per unit mass required to raise the temperature by 1 K as a function in of position and temperature.
And u(x,t) is the temperature as a function of position and time.
So I would’ve thought that the energy per unit mass required to raise the temperature to u(x,t) would be the desired temperature (u(x,t)) multiplied by the specific heat (c(x,u(x,t))).
This would give me u(x,t)c(x,u(x,t))), which is not what they’re looking for, and is very close to what they explicitly say is an incorrect answer.
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