Notes: Please i need help in this question thank you.A cube of cooper 2.00cm on a side is suspended by a string. The cube is heated with a burner from...

Saturday, March 30, 2013

Please i need help in this question thank you.A cube of cooper 2.00cm on a side is suspended by a string. The cube is heated with a burner from...

The volume of the cube is

$\displaystyle{V}$
= d^3 =0.02^3 =8*10^-6 m^3

The coefficient of volumetric
expansion for copper is $\displaystyle\gamma={5.1}\cdot{{10}}^{{-{{6}}}}{{K}}^{{-{{1}}}}$

The
increase in temperature is $\displaystyle\delta{\left({T}\right)}={90}-{20}={70}{K}={70}\circ{C}$

The law of volume variation with temperature
is

$\displaystyle\delta{\left({V}\right)}=\gamma\cdot{V}\cdot\delta{\left({T}\right)}={5.1}\cdot{{10}}^{{-{{6}}}}\cdot{8}\cdot{{10}}^{{-{{6}}}}\cdot{70}$
=2.856*10^-9 m^3

$\displaystyle\delta{\left({V}\right)}={2.856}\cdot{{10}}^{{-{{3}}}}{c}{{m}}^{{3}}$

The mechanical work done
by the cube to increase its volume against the atmospheric pressure
is

$\displaystyle{W}={P}\cdot\delta{\left({V}\right)}={1.01}\cdot{{10}}^{{5}}\cdot{2.856}\cdot{{10}}^{{-{{9}}}}={2.885}\cdot{{10}}^{{-{{4}}}}{J}$

The mass of the cube
is

$\displaystyle{m}=\rho\cdot{V}={8900}\cdot{8}\cdot{{10}}^{{-{{6}}}}={7.12}\cdot{{10}}^{{-{{2}}}}{k}{g{=}}{71.2}{g{{r}}}{a}{m}{s}$

The heat necessary to increase the temperature of the cube
is

$\displaystyle{Q}={m}\cdot{C}{p}\cdot\delta{\left({T}\right)}={7.12}\cdot{{10}}^{{-{{2}}}}\cdot{390}\cdot{70}={1943.76}{J}$

d) If $\displaystyle{U}$ is the internal energy of the cube then the
first principle of thermodynamics says:

$\displaystyle{Q}=\delta{\left({U}\right)}+{W}$

$\displaystyle\delta{\left({U}\right)}={Q}-{W}={1943.76}-{2.885}\cdot{{10}}^{{-{{4}}}}={1943.7597}{J}$

Notes

Saturday, March 30, 2013

Please i need help in this question thank you.A cube of cooper 2.00cm on a side is suspended by a string. The cube is heated with a burner from...

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