The combustion of 0.25 moles of octane gas (C8H18) to CO2 gas and H2O gas (vapor) against a constant, external pressure of 1.9 atm increases the total volume of gas from 113.1 L to 148.5 L. How much work is performed by this expansion?

Respuesta :

Answer: The work done for the given process is -6813.44 J

Explanation:

To calculate the amount of work done for an isothermal process is given by the equation:

[tex]W=-P\Delta V=-P(V_2-V_1)[/tex]

W = amount of work done = ?

P = pressure = 1.9 atm

[tex]V_1[/tex] = initial volume = 113.1 L

[tex]V_2[/tex] = final volume = 148.5 L

Putting values in above equation, we get:

[tex]W=-1.9atm\times (148.5-113.1)L=-67.26L.atm[/tex]

To convert this into joules, we use the conversion factor:

[tex]1L.atm=101.33J[/tex]

So, [tex]-67.26L.atm=-67.26\times 101.3=-6813.44J[/tex]

The negative sign indicates the system is doing work.

Hence, the work done for the given process is -6813.44 J

The work done for the given process is -6813.44 J

Calculation of work done:

To calculate the amount of work done for an isothermal process is given by the equation:

[tex]W=-P\triangle V=-P(V_2-V_1)[/tex]

where,

W = amount of work done = ?

P = pressure = 1.9 atm

V₁ = initial volume = 113.1 L

V₂ = final volume = 148.5 L

On substituting the values:

[tex]W=-1.9atm*(148.5-113.1)L\\\\W=62.26Latm[/tex]

The negative sign shows the system is doing work.

Hence, the work done for the given process is -6813.44 J.

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