An ideal gas of mass $m$ and temperature $T_{1}$ undergoes a reversible isothermal process from an initial pressure $P_{1}$ to final pressure $P_{2}$. The heat loss during the process is $Q$. The entropy change $\Delta S$ of the gas is

(A) $m R \ln \left(\frac{P_{2}}{P_{1}}\right)$

(B) $m R \ln \left(\frac{P_{1}}{P_{2}}\right)$

(C) $m R \ln \left(\frac{P_{2}}{P_{1}}\right)-\frac{Q}{T_{1}}$

(D) zero

An ideal gas of mass $m$ and temperature $T_{1}$ undergoes a reversible isothermal process from an initial pressure $P_{1}$ to final pressure $P_{2}$. The heat loss during the process is $Q$. The entropy change $\Delta S$ of the gas is

(A) $m R \ln \left(\frac{P_{2}}{P_{1}}\right)$

(B) $m R \ln \left(\frac{P_{1}}{P_{2}}\right)$

(C) $m R \ln \left(\frac{P_{2}}{P_{1}}\right)-\frac{Q}{T_{1}}$

(D) zero

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