Thermodynamic processes

For the P-V diagram given for an ideal gas,

out of the following which one correctly represents the T-P diagram ?

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

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by $PV^n$ = constant, then n is given by (Here $C_P$ and $C_V$ are molar specific heat at constant pressure and constant volume, respectively) :

'n' moles of an ideal gas undergoes a process A→B as shown in the figure. The maximum temperature of the gas during the process will be :

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is :

Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $u=\dfrac UV\propto T^4$ and pressure $p=\dfrac13\left(\dfrac UV\right)$. If the shell now undergoes an adiabatic expansion the relation between T and R is :

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $V^q$, where V is the volume of the gas. The value of q is :
$$\left(\gamma=\frac{C_p}{C_v}\right)$$

An ideal gas goes through a reversible cycle a→b→c→d has the V - T diagram shown below. Process d→a and b→c are adiabatic.

The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) :

A thermodynamic system is taken from an initial state $i$ with internal energy $U_i=100$ J to the final state $f$ along two different paths $iaf$ and $ibf$, as schematically shown in the figure. The work done by the system along the paths $af$, $ib$ and $bf$ are $W_{af}=200$ J, $W_{ib}=50$ J and $W_{bf}=100$ J respectively. The heat supplied to the system along the path $iaf$, $ib$ and $bf$ are $Q_{iaf}$, $Q_{ib}$ and $Q_{bf}$ respectively. If the internal energy of the system in the state $b$ is $U_b=200$ J and $Q_{iaf}=500$ J, the ratio $Q_{bf}/Q_{ib}$ is

Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. Then total work done by the gases till the time they achieve equilibrium will be

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement :

During an adiabatic compression, 830 J of work is done on 2 moles of a diatomic ideal gas to reduce its volume by 50%. The change in its temperature is nearly : ($R=8.3$ JK$^{-1}$ mol$^{-1}$)

An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section $8.0\times10^{-3}$ m$^2$. Initially the gas is at 300K and occupies a volume of $2.4\times10^{-3}$ m$^3$ and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is $1.0\times10^5$ N/m$^2$. The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be :

(Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible)

One mole of a monatomic ideal gas is taken along two cyclic processes E→F→G→E and E→F→H→E as shown in the PV diagram. The processes involved are purely isochoric, isobaric, isothermal or adiabatic.

Match the paths in List I with the magnitudes of the work done in List II and select the correct answer using the codes given below the lists.

Two moles of ideal helium gas are in a rubber balloon at 30 °C. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to 35 °C. The amount of heat required in raising the temperature is nearly (take $R=8.31$ J/mol.K)

5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be $T_1$, the work done in the process is

One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II gives the characteristics involved in the cycle. Match them with each of the processes given in Column I.

One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is $P_0$. Choose the correct option(s) from the following

A diatomic ideal gas is compressed adiabatically to $\dfrac1{32}$ of its initial volume. In the initial temperature of the gas is $T_i$ (in Kelvin) and the final temperature is $aT_i$, the value of $a$ is

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,