Question 205: Thermodynamics & KTG

Question

The initial pressure and volume of an ideal gas are P$_0$ and V$_0$. The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_0}{4}$ will be :
(Given $\gamma$ = ratio of specific heats at constant pressure and at constant volume)

Accepted Answer

When the gas is compressed suddenly, it undergoes an adiabatic process where no heat is exchanged with the surroundings.
Therefore, we can use the adiabatic equation of state to relate the initial and final pressure and volume of the gas: $P_0V_0^\gamma=P_fV_f^\gamma$ where $P_f$ and $V_f$ are the final pressure and volume of the gas, respectively.
Since the gas is compressed to $\frac{V_0}{4}$, we have: $V_f=\frac{V_0}{4}$ Substituting this into the adiabatic equation of state, we get: $P_f=P_0\left(\frac{V_0}{V_f}\right)^\gamma=P_0\left(\frac{4}{1}\right)^\gamma=4^\gamma P_0$
Therefore, the final pressure of the gas when it is suddenly compressed to $\frac{V_0}{4}$ is $4^\gamma P_0$.

Answer

P$_0$(4)$^{\frac{1}{\gamma}}$

Answer

P$_0$

Answer

4P$_0$

Answer

P$_0$(4)$^{\gamma}$

Thermodynamics & KTG

The initial pressure and volume of an ideal gas are P_0 and V_0. The final pressure of the gas when the gas is suddenly compressed to volume \frac{V_0}{4} will be : (Given \gamma = ratio of specific heats at constant pressure and at constant volume)

Choose the correct answer: