Chapter 13, Problem 15P

To determine

(a) To determine:

The coefficient of volume expansion of the container

Answer to Problem 15P

Solution:

The coefficient of volume expansion of the container is $5\times {10}^{-5}\frac{1}{°C}$

Explanation of Solution

Given:

Initial volume of water,$V_i=55.5mL$

Initial volume of the container, $V_i=55.5mL$

Initial temperature, $T_i=20°C$

Final temperature, $T_f=60°C$

Mass of water lost from the container on being heated, $m_w=0.35g$

Density of water at 60°C, ${\rho }_w=0.98324\frac{g}{mL}$

Formula used:

$\Delta V=\beta V_i\Delta T$, where V_i is the initial volume and β is the coefficient of volume expansion

$V=\frac{m}{\rho }$

Calculation:

The relation between change in volume of a substance (ΔV)and change in temperature (ΔT)is given by,

$\Delta V=\beta V_i\Delta T$--- (i),

Where, V_i is the initial volume and β is the coefficient of volume expansion

In this case, the volume of water lost, $\Delta V=\Delta V_w–\Delta V_c$--- (ii),

Where, ΔV_wis the change in volume of water and ΔV_c is the change in volume of the container

Since volume = $\frac{m}{\rho }$, where m is mass and ρ is density

The volume of water lost, $\Delta V=\frac{m_w}{{\rho }_w}$--- (iii)

From equation (i),

$\Delta V_w={\beta }_w{V}_i\left(T_f–T_i\right)$---(iv)

$\Delta V_c={\beta }_c{V}_i\left(T_f–T_i\right)$---(v)

${\beta }_w=210\times {10}^{-6}\frac{1}{°C}$

From equations (ii), (iii), (iv)and (v)

$\frac{m_w}{{\rho }_w}= {\beta }_w{V}_i\left(T_f–T_i\right)-{\beta }_c{V}_i\left(T_f–T_i\right)$

Substituting all the known values,

$\frac{0.35\text{}g}{0.98324\frac{g}{mL}}=\left(60°C-20°C)\left(55.5mL\right)(210\times {10}^{-6}\frac{1}{°C}–{\beta }_c\right)$

or $(210\times {10}^{-6}\frac{1}{°C}–{\beta }_c)=1.6\times {10}^{-4}\frac{1}{°C}$

or ${\beta }_c=5\times {10}^{-5}\frac{1}{°C}$

To determine

(b) To determine:

The most likely material of the container

Answer to Problem 15P

Solution:

The most likely material of the container is copper.

Explanation of Solution

Based on the standard values of coefficient of volume expansion for solids, the most likely material of the container is copper.