The expansion process of `v = 2.0` moles of argon proceeds so that the gas pressure increases in direct alphaortion to its volume. Find the entropy increment of the gas in this process provided its volume increases `alpha = 2.0`times.

Explanation

The process in question may be written as
`(p)/(p_0) = alpha (V)/(V_0)`
where `alpha` is a constant and `p_0, V_0` are some reference values. For this process (see 2.127) the specific heat is
`C = C_V + (1)/(2) R = R ((1)/(gamma - 1) + (1)/(2)) = (1)/(2) R (gamma + 1)/(gamma - 1)`
Along the line volume increases `alpha` times then so does so does the pressure. The temperature must then increase `alpha^2` times. Thus
`Delta S = int _(T_0)^(alpha^2 T_0) vC (dT)/(T) = (vR)/(2) (gamma + 1)/(gamma - 1) 1n alpha^2 = vR (gamma + 1)/(gamma - 1) 1n alpha`
if `v = 2, gamma = (5)/(3), alpha = 2, Delta S = 46.1 "Joule"//.^@K`.