Work done by a gas

A vessel contains 0.15 m³ of a gas at pressure 8 bar and temperature 140 °C with $c_p=3R$ and $c_v=2R$. It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is ________ kJ. ($R$ is gas constant)

A certain gas is isothermally compressed to $\left(\dfrac13\right)^{\text{rd}}$ of its initial volume ($V_o=3$ litre) by applying required pressure. If the bulk modulus of the gas is $3\times10^5$ N/m², the magnitude of work done on the gas is ________ J.

One mole of a monatomic ideal gas undergoes the cyclic process J→K→L→M→J, as shown in the P-T diagram.

Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

[$\mathcal{R}$ is the gas constant.]

One mole of an ideal gas undergoes two different cyclic processes I and II, as shown in the $P$-$V$ diagrams below. In cycle I, processes $a, b, c$ and $d$ are isobaric, isothermal, isobaric and isochoric, respectively. In cycle II, processes $a', b', c'$ and $d'$ are isothermal, isochoric, isobaric and isochoric, respectively. The total work done during cycle I is $W_I$ and that during cycle II is $W_{II}$. The ratio $W_I/W_{II}$ is _____.

In the given $P$-$V$ diagram, a monoatomic gas $\left(\gamma = \frac53\right)$ is first compressed adiabatically from state $A$ to state $B$. Then it expands isothermally from state $B$ to state $C$. [Given: $\left(\frac13\right)^{0.6} \simeq 0.5$, $\ln 2 \simeq 0.7$].

Which of the following statement(s) is(are) correct?

Given below are two statements :

Statement I : When $\mu$ amount of an ideal gas undergoes adiabatic change from state $(P_1,V_1,T_1)$ to state $(P_2,V_2,T_2)$, then work done is $W=\dfrac{\mu R(T_2-T_1)}{1-\gamma}$, where $\gamma=\dfrac{C_P}{C_V}$ and R = universal gas constant.

Statement II : In the above case, when work is done on the gas, the temperature of the gas would rise.

Choose the correct answer from the options given below:

Starting with the same initial conditions, an ideal gas expands from volume $V_1$ to $V_2$ in three different ways. The work done by the gas is $W_1$ if the process is purely isothermal, $W_2$, if the process is purely adiabatic and $W_3$ if the process is purely isobaric. Then, choose the correct option

A sample of monoatomic gas is taken at initial pressure of 75 kPa. The volume of the gas is then compressed from 1200 cm$^3$ to 150 cm$^3$ adiabatically. In this process, the value of workdone on the gas will be :

A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be

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 :

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 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 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?

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)

A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure $P_i=10^5$ Pa and volume $V_i=10^{-3}\ \mathrm m^3$ changes to a final state at $P_f=(1/32)\times10^5$ Pa and $V_f=8\times10^{-3}\ \mathrm m^3$ in an adiabatic quasi-static process, such that $P^3V^5=$ constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at $P_i$ followed by an isochoric (isovolumetric) process at volume $V_f$. The amount of heat supplied to the system in the two-step process is approximately