On mole of argon expands polytropically, the polytropic constant being 1.5, that is, the process proceeds according to the law `pV^(1.5)` = constant. In the process, its temperature change by `Delta T = - 26 K`. Find
a. the amount of heat obatined by the gas.
b. the work performed by the gas.

Explanation

(a) Increment of internal energy for `Delta T`, becomes
`Delta u = (v R Delta T)/(gamma - 1) = (R Delta T)/(gamma - 1) = -324 J(as v = 1 "mole")`
From first law of thermodynamics
`Q = Delta U + A (R Delta T)/(gamma - 1) - (R Delta T)/(n - 1) = 0.11 kJ`
(b) Sought work done, `A_n = int pdV = int_(V_i)^(V_f) (k)/(V^n) dV`
(where `pV^n = k = p_i V_i^n = p_f V_f^n`)
`(k)/(1-n)(V_f^(1 -n) - V_i^(1 - n)) = ((p_f V_f^n V_f^(1-n) -p_i V_i^n V_i^(1- n)))/(1 - n)`
=`(p_f V_f - p_i V_i)/(1 - n) = (vR(T_f - T_i))/(1 -n)`
=`(v R Delta T)/(n - 1) = -(R Delta T)/(n - 1) = 0.43 kJ(as v = 1 "mole")`.