Question

Two gases have the same initial pressure, volume and temperature. They expand to the same final volume, one adiabatically and the other isothermally. Which of the following statements is correct?

• A. The final temperature is greater for the isothermal process
• B. The final pressure is greater for the isothermal process
• C. The work done by the gas is greater for the isothermal process
• D. All the above options are incorrect

Answer 1

Answer: (A), (B), (C)

The correct options are
A The final temperature is greater for the isothermal process
B The final pressure is greater for the isothermal process
C The work done by the gas is greater for the isothermal process

Work done is equal to area under the P-V graph, thus work done by gas is greater for isothermal process.

For isothermal process: $T_2=T_o$

For adibatic process: $T_o(V_o{)}^{\gamma -1}=T(V{)}^{\gamma -1}$

As $V>V_o⟹T<T_o$

Thus final temp. is greater for isothermal process.

For isothermal process: $P_o{V}_o=P_{i}V⟹P_i=P_o\frac{V_o}{V}$

For adibatic process: $P_o(V_o{)}^{\gamma }=P_a(V{)}^{\gamma }$

$⟹P_a=P_o(\frac{V_o}{V}{)}^{\gamma }$

As $\gamma >1$ (always) $⟹P_i>P_a$