A sample of a solid substance has a mass m and a density ?0 at a temperature T0. (a) Find the density of the substance if its temperature is increased by an amount ?T in terms of the coefficient of volume expansion ?. (Use any variable or symbol stated above as necessary.) (b) What is the mass (m') of the sample if the temperature is raised by an amount ?T? (Use any variable or symbol stated above as necessary.)

Question

anonymous · Answer

The mass of the sample will remain constant i.e. m independent of the temperature. This is the answer of part (b).  m'=m

Initial temperature was T$_{0}$ Let densities and volume be d(T$_{0}$) and V(T$_{0}$) respectively at  T$_{0}$.

Finally temperature = T+ T$_{0}$ Let volume and densities at this temperature be d(T$_{0}$+T) and  V(T$_{0}$+T).

V (T$_{0}$+T)=V( T$_{0}$)[1+$\gamma$T]

where $\gamma$ is coefficient of thermal expansion and T is change in temperature of solid.

volume=mass/density

So,  $\huge{\frac{m}{d( T_{0}+T)} =\frac{m}{d(T_{0})}[1+\gamma T]}$

From this,

$\huge{d(T_{0}+T)=\frac{d(T_{0})}{[1+\gamma T]}}$

Density has decreased as it should!