Question

A piece of aluminum has a volume of 3.94 x 10-3 m3. The coefficient of volume expansion for aluminum is = 69 x 10-6(C°)-1. The temperature of this object is raised from 1.20 to 311 oC. How much work is done by the expanding aluminum if the air pressure is 1.01 x 105 Pa?

Answer 1

hint:
first, we have to compute the final volume, which is given by the subsequent formula:
\[\Large {V_1} = {V_0}\left( {1 + 3\lambda \Delta t} \right)\]
where:
\[\Large \begin{gathered}
\lambda = 69 \cdot {10^{ - 6}}\;{\left( {^\circ C} \right)^{ - 1}},\quad \Delta t = 311 - 1.2 = ...^\circ C \hfill \\
\quad \hfill \\
{V_0} = 3.94 \cdot {10^{ - 3}}{m^3} \hfill \\
\end{gathered} \]
second step:
the requested work L, done by the system, namely done by our cube of aluminum, is:
\[\Large L = {P_0}\left( {{V_1} - {V_0}} \right)\]