Three samples $X, Y$,and $Z$ of the same gas have equal volumes and temperatures. The volume of each sample is doubled. The process is isothermal for $X$,adiabatic for $Y$,and isobaric for $Z$. If the final pressures are equal for the three samples,find the ratio of the initial pressures. (Take adiabatic exponent $\gamma = 3/2$)

Is the splitting of water an exothermic or an endothermic process?

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?
$(A)$ Process $I$ is an isochoric process
$(B)$ In process $II$,gas absorbs heat
$(C)$ In process $IV$,gas releases heat
$(D)$ Processes $I$ and $III$ are $not$ isobaric

The following figure shows the $P-T$ graph for four processes $A, B, C,$ and $D$. Select the correct alternative.

An ideal gas with pressure $P$,volume $V$ and temperature $T$ is expanded isothermally to a volume $2V$ and a final pressure $P_i$. The same gas is expanded adiabatically to a volume $2V$,the final pressure is $P_a$. In terms of the ratio of the two specific heats for the gas $\gamma$,the ratio $\frac{P_i}{P_a}$ is

$A$ heating element of resistance $r$ is fitted inside an adiabatic cylinder which carries a frictionless piston of mass $m$ and cross-sectional area $A$. The cylinder contains one mole of a diatomic gas. The temperature of the gas varies with time $t$ as $T = \alpha t + \frac{1}{2} \beta t^2$ (where $\alpha$ and $\beta$ are constants),while the pressure remains constant. The atmospheric pressure above the piston is $P_0$. Then: