Respuesta :
Answer:
-4728.49 J
Explanation:
It is an Adiabatic process. For an adiabatic process, work done can be calculated as follows:
[tex]W= \fracC{V_1^{1-n}-V_2^{1-n}}{n-1}[/tex]
[tex]PV^n = C\\ (350 kPa)(0.03m^3)^{1.5}=1818.65[/tex]
Substitute the values:
[tex]W=(1818.65)\frac{(0.03^{(1-1.5)}-0.02^{(1-1.5)})}{(1.5-1)} = (1818.65)\frac{(5.77-7.07)}{0.5}=-4728.49[/tex]
Work done by piston–cylinder devices, when gas expands during expansion and compression processes is -4728.49 joules.
What is adiabatic process?
Adiabatic process is the process in which, their is no heat transfer throughout the process.
In a adiabatic process the gases satisfy the following relationship as,
[tex]PV^n= C[/tex]
The work done of a adiabatic process is given as,
[tex]W=C\times\dfrac{V_f^{(1-n)}-V_i^{(1-n)}}{1-n}[/tex]
Here, (n) and (C) are constants.
For the given situation the gases have been observed to satisfy the relationship
[tex]PV^n= C[/tex]
As the gas expands from 350 k-Pa and 0.03 m³. Thus the value of initial pressure is 350 k-Pa and the value of initial volumes 0.03 m³ .
The final volume is 0.2 m³ and the constant n is 1.5.Put the values to find the value of constant as,
[tex](350)(0.03)^{1.5}= C\\C=1818.65[/tex]
Put this value of constant in the formula of work done as,
[tex]W=(1818.65)\times\dfrac{(0.03)^{(1-(1.5))}-(0.02)^{(1-(1.5))}}{1-(1.5)}\\W=-4728.49\rm J[/tex]
Thus, the work done is -4728.49 joules.
Lean more about the adiabatic process here;
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