Respuesta :
Answer:
[tex]dV=4.1136\times 10^{-4}\ m^3[/tex]
Explanation:
Given:
- Mass of the bricks carried, [tex]m=207\ kg[/tex]
- height of displacement, [tex]h=3.65\ m[/tex]
- Constant pressure of the gas, [tex]P=1.8\times 10^6\ Pa[/tex]
Now the work done to displace the brick along the length of the ladder:
[tex]W=(m.g)\times h[/tex]
[tex]W=(207\times 9.8)\times 3.65[/tex]
[tex]W=740.439\ J[/tex]
As we know that the work done in compressing the gas at constant pressure is given as:
[tex]W=P.dV[/tex]
where:
[tex]dV=[/tex] change in volume of the gas
[tex]740.439=1.8\times 10^6\times dV[/tex]
[tex]dV=4.1136\times 10^{-4}\ m^3[/tex]
The change in volume of the gas is [tex]4.1177\times10^{-3}\ m^3[/tex].
Given to us:
Mass of the brick m= 207 kg,
Height at which brick is displaced h= 3.65 m,
constant pressure p = [tex]1.8 X 10^6[/tex] Pa,
Acceleration due to gravity g=9.81 m/s²
To find out the work done by Russell to displace the brick,
[tex]\rm work\ done, w= (mgh)[/tex]
putting the numerical values we get,
[tex]\begin{aligned}w&=mgh\\&=207\times9.81\times3.65\\&= 7411.9455\ \rm J\\\end{aligned}[/tex]
For a constant pressure process work done is given by,
[tex]\begin{aligned}w&=p\delta v\\7411.9455&=1.8\times 10^6\times\delta v\\\delta v&=0.0041177\ m^3\\\delta v&=4.1177\times10^{-3}\ m^3\end{aligned}[/tex]
Hence, the change in volume of the gas is [tex]4.1177\times10^{-3}\ m^3[/tex].
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