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

The cycle shown in the figure represents an engine (the engine consists of one mole of gas in a cylinder with a piston). $A$ to $B$ is isochoric,$B$ to $C$ is isothermal,$C$ to $D$ is isochoric,and $D$ to $A$ is isothermal. Also,$V_C = V_D = 2V_A = 2V_B$.
$(a)$ In which part of the cycle is heat supplied to the engine from the outside?
$(b)$ In which part of the cycle can the engine give energy to its surroundings?
$(c)$ How much work is done by the engine during one cycle? Give your answer in terms of $P_A, P_B$ and $V_A$.
$(d)$ What is the efficiency of the engine? (For the gas,$\gamma = 5/3$,and for one mole,$C_V = 3/2 R$)

An ideal gas undergoes a cyclic process through various thermodynamic states. The heat energy $(Q)$ and work $(W)$ associated with these states are given as follows:
$Q_1 = 6000 \ J, Q_2 = -5500 \ J, Q_3 = -3300 \ J, Q_4 = 3500 \ J,$
$W_1 = 2500 \ J, W_2 = -1000 \ J, W_3 = -1200 \ J, W_4 = x \ J$
If the ratio of the net work done to the net heat absorbed is $\eta$, then the values of $x$ and $\eta$ are respectively:

What is an isochoric process and a cyclic process? Write the first law of thermodynamics for an ideal gas.

The figure shows the $P-V$ plot of an ideal gas taken through a cycle $ABCDA$. The part $ABC$ is a semi-circle and $CDA$ is half of an ellipse. Then,
$(A)$ the process during the path $A \rightarrow B$ is isothermal
$(B)$ heat flows out of the gas during the path $B \rightarrow C \rightarrow D$
$(C)$ work done during the path $A \rightarrow B \rightarrow C$ is zero
$(D)$ positive work is done by the gas in the cycle $ABCDA$

$A$ cyclic process $ABCD$ is shown in the given $P-V$ diagram. Which of the following diagrams represents the same process in a $P-T$ graph?