## Calculate wa, the work done by the gas as it expands along path a from v0 to va=rvv0. express wa in terms of p0, v0, and rv

Question

Calculate wa, the work done by the gas as it expands along path a from v0 to va=rvv0. express wa in terms of p0, v0, and rv

in progress 0

1. W= Integral of P dV
PV = nRT
P= PO VO/ V
W= Integral of PO VO/ v dV
W= PO VO In (Vf/VO)
So we can say that,
W= PO VO In Rv

2. The work done by the gas is :

### Wa = Po Vo ( Rv – 1 )

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### Further explanation

The Ideal Gas Law that needs to be recalled is:

[tex]large {boxed {PV = nRT} }[/tex]

P = Pressure (Pa)

V = Volume (mu00b3)

n = number of moles (moles)

R = Gas Constant (8.314 J/mol K)

T = Absolute Temperature (K)

Let us now tackle the problem !

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Complete Question:

Calculate [tex]W_A[/tex], the work done by the gas as it expands along path A from [tex]V_0[/tex] to [tex]V_A = R_V V_0[/tex].

Express [tex]W_A[/tex in terms of [tex]p_0 , V_0,[/tex] and [tex]R_V[/tex]

Given:

initial volume = Vo

final volume = V_A

constant pressure = p_o

word done by the gas = W_A = ?

Solution:

Work done by the gas is the area under Pressure Vs Volume Graph.

[tex]texttt{Work} = texttt{Area Under P Vs V Graph}[/tex]

[tex]W_A = p_0 times ( V_A – V_0 )[/tex]

[tex]W_A = p_0 times ( R_V V_0 – V_0 )[/tex]

[tex]W_A = p_0 V_0 times ( R_V – 1 )[/tex]

[tex]large {boxed {W_A = p_0 V_0 ( R_V – 1 )} }[/tex]

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