Thermodynamic processes

A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be :

The pressure P$_1$ and density d$_1$ of diatomic gas $\left(\gamma=\dfrac75\right)$ changes suddenly to P$_2$ (> P$_1$) and d$_2$ respectively during an adiabatic process. The temperature of the gas increases and becomes _______ times of its initial temperature. (given $\dfrac{d_2}{d_1}=32$)

An ideal gas undergoes a four step cycle as shown in the $P-V$ diagram below. During this cycle, heat is absorbed by the gas in

The value of $\dfrac{T_R}{T_0}$ is

The value of $\dfrac{Q}{RT_0}$ is

n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.

A → B : Isothermal expansion at temperature T so that the volume is doubled from V$_1$ to V$_2$ = 2V$_1$ and pressure changes from P$_1$ to P$_2$.

B → C : Isobaric compression at pressure P$_2$ to initial volume V$_1$.

C → A : Isochoric change leading to change of pressure from P$_2$ to P$_1$.

Total workdone in the complete cycle ABCA is :

Match List I with List II.

Choose the correct answer from the options given below :

Consider one mole of helium gas enclosed in a container at initial pressure $P_1$ and volume $V_1$. It expands isothermally to volume $4V_1$. After this, the gas expands adiabatically and its volume becomes $32V_1$. The work done by the gas during isothermal and adiabatic expansion processes are $W_{iso}$ and $W_{adia}$, respectively. If the ratio $\dfrac{W_{iso}}{W_{adia}} = f\ln 2$, then $f$ is ______.

A spherical bubble inside water has radius $R$. Take the pressure inside the bubble and the water pressure to be $p_0$. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes $(R - a)$. For $a \ll R$ the magnitude of the work done in the process is given by $(4\pi p_0 R a^2)X$, where $X$ is a constant and $\gamma = C_p/C_V = 41/30$. The value of $X$ is ______.

One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature $(V$-$T)$ diagram. The correct statement(s) is/are:

[$R$ is the gas constant]

A mixture of ideal gas containing 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure $P_0$, volume $V_0$, and temperature $T_0$. If the gas mixture is adiabatically compressed to a volume $V_0/4$, then the correct statement(s) is/are,

(Given $2^{1.2} = 2.3$; $2^{3.2} = 9.2$; $R$ is gas constant)

If the process carried out on one mole of monatomic ideal gas is as shown in figure in the $PV$-diagram with $P_0V_0 = \frac13RT_0$, the correct match is,

If the process on one mole of monatomic ideal gas is as shown in the $TV$-diagram with $P_0V_0 = \frac13RT_0$, the correct match is,

One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where $V$ is the volume and $T$ is the temperature). Which of the statements below is (are) true?

One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is 100 K and the universal gas constant $R = 8.0\ \mathrm{J\,mol^{-1}\,K^{-1}}$, the decrease in its internal energy, in Joule, is__________.

One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the $PV$-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-1 with the corresponding statements in List-II.

Which of the following options is the only correct representation of a process in which $\Delta U = \Delta Q - P\Delta V$?

Which one of the following options is the correct combination?

Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?

An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is :

(Take $C_v=1.5$ R, where R is gas constant)