An ideal gas of mass m in a state A goes to another state B `Vialpha` three different processes as shown in figure. If `Q_(1),Q_(2)and Q_(3)` denote the heat absorbed by the gas along the three paths,then

Options

A. `Q_1 lt Q_2 lt Q_3`
B. `Q_1 lt Q_2 = Q_3`
C. `Q_1 = Q_2 gt Q_3`
D. `Q_1 gt Q_2 gt Q_3`

Answer

A

Explanation

`f_("mix") = (n_1 f_1 + n_2 f_2)/(n_1 + n_2) = (2xx5+3 xx3)/(2+3) = 19//5" & "f_("min")/2 = 1/(gamma _("mix")-1)`
` rArr " "19/10 = 1/(gamma_("mix")-1) "and "C_V = (fR)/2 = 1.9R " & "C_p = C_r+ R = 2.9 R " & "gamma_("mix") = 29//19 ~~1.53`
`P_1 V_1^gamma = P_2 V_2^gamma " "rArr" "P_a V^(1.53) = (2V)^(1.53) rArr P =P_a/2^(1.53)`