Question 36: Thermodynamics & KTG

Question

A given volume of gas at NTP is allowed to expand 6 times of its original volume, first under isothermal condition and then under adiabatic condition. Which of the given statement is correct? [Given $\frac{c_p}{c_v}=\gamma=1.4$ ]

Accepted Answer

LetÃ¢ÂÂs compare the two final pressures, starting from the same initial state $(p_1,V_1,T_1)$ and expanding to $V_2=6V_1$.
Isothermal expansion
Ã¢ÂÂ¢ Temperature stays at $T_1$.
Ã¢ÂÂ¢ By BoyleÃ¢ÂÂs law:
$$p_{2,\rm iso} \;=\;\frac{p_1\,V_1}{V_2}         \;=\;\frac{p_1}{6}\,. $$
Adiabatic expansion
Ã¢ÂÂ¢ No heat exchange, so
$$p_1\,V_1^\gamma \;=\;p_{2,\rm ad}\,V_2^\gamma        \quad\Longrightarrow\quad        p_{2,\rm ad}        \;=\;p_1\Bigl(\frac{V_1}{V_2}\Bigr)^\gamma        \;=\;p_1\;6^{-\gamma}\,. $$
Ã¢ÂÂ¢ With $\gamma=1.4$:
$$6^{-1.4}\approx\frac1{6^{1.4}}\approx\frac1{12.3}\approx0.08        \quad\Longrightarrow\quad        p_{2,\rm ad}\approx0.08\,p_1\,. $$
Since $p_{2,\rm ad}\approx0.08\,p_1$ is smaller than $p_{2,\rm iso}=0.167\,p_1$, the final pressure after adiabatic expansion is lower than after isothermal expansion.
Answer: Option D.

Answer

The final pressure after the adiabatic expansion is 1.4 times greater than the final pressure after the isothermal expansion.

Answer

The final temperature after the adiabatic expansion is 1.4 times less than the final temperature after the isothermal expansion.

Answer

Pressure remains same in both adiabatic and isothermal expansion

Answer

The final pressure after the adiabatic expansion is less than the final pressure after the isothermal expansion.

Thermodynamics & KTG

A given volume of gas at NTP is allowed to expand 6 times of its original volume, first under isothermal condition and then under adiabatic condition. Which of the given statement is correct? [Given \frac{c_p}{c_v}=\gamma=1.4 ]

Choose the correct answer: