Question

During an isothermal compression process, entropy of a fixed mass if ideal gas

Answer 1

in isothermal compression change in internal energy equals to zero.
from first law of thermodynamics,
∆Q = ∆U + w
∆Q = w

w = PdV
= $\frac{nRT}{V}dv$
= $nRT\int\limits^{V_f}_{V_i}\frac{dV}{V}$
=$nRT ln\frac{V_f}{V_i}$

so, ∆Q = $nRT ln\frac{V_f}{V_i}$
now, entropy = $\frac{\Delta Q}{T}$
=$nR ln\frac{V_f}{V_i}$

hence During an isothermal compression process, entropy of a fixed mass is $nR ln\frac{V_f}{V_i}$ if ideal gas