The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order, is given by:

   
1. \(d,~a,~b,~c\)
2. \(a,~d,~c,~b\)
3. \(a,~d,~b,~c\)
4. \(d,~a,~c,~b\)

The following figure shows two processes \(A\) and \(B\) for a gas. If \(\Delta Q_A\) and \( \Delta Q_B\) are the amount of heat absorbed by the system in two cases, and \(\Delta U_A\) and \(\Delta U_B\) are changes in internal energies, respectively, then:

When heat \(Q\) is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by \(\Delta T\). the heat required to produce the same change in temperature, at a constant pressure is:
1. \( \frac{7}{5} Q \)
2. \(\frac{3}{2} Q \)
3. \( \frac{2}{3} Q \)
4. \( \frac{5}{3} Q\)
 

A cylinder with fixed capacity of \(67.2\) litres contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by \(20^\circ \text{C}\) is: [Given that \(R = 8.31\) J mol^–1K^–1]
1. \(748~\text{J}\)
2. \(350~\text{J}\)
3. \(374~\text{J}\)
4. \(700~\text{J}\)

\(n\) moles of an ideal gas with constant volume heat capacity \(C_V\) undergo an isobaric expansion by a certain volume. The ratio of the work done in the process, to the heat supplied is:
1. \( \dfrac{n R}{C_V+n R} \)

2. \( \dfrac{n R}{C_V-n R} \)

3. \( \dfrac{4 n R}{C_V+n R} \)

4. \( \dfrac{4 n R}{C_V-n R}\) 

A diatomic gas with rigid molecules undergoes expansion at constant pressure, performing \(10~\text{J}\) of work in the process. What is the amount of heat energy absorbed by the gas during this process?
1. \(35~\text{J}\)
2. \(40~\text{J}\)
3. \(25~\text{J}\)
4. \(30~\text{J}\)

A sample of an ideal gas is taken through the cyclic process \(abca\) as shown in the figure. The change in the internal energy of the gas along the path \(ca\) is \(-180~\text{J}\). The gas absorbs \(250~\text{J}\) of heat along the path \(ab\) and \(60~\text{J}\) along the path \(bc\). The work done by the gas along the path \(abc\) is:

1. \(140~\text{J}\)
2. \(130~\text{J}\)
3. \(100~\text{J}\)
4. \(120~\text{J}\)

Two moles of helium gas are mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of the mixture at constant volume? (\(R = 8.3~\text{J/mol K}\))
1. \(21.6~\text{J/mol K}\)
2. \(19.7~\text{J/mol K}\)
3. \(15.7~\text{J/mol K}\)
4. \(17.4~\text{J/mol K}\)

An engine takes in \(5\) moles of air at \(20^\circ\) C and \(1\) atm, and compresses it adiabaticaly to \(1/10\) th of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be:
1. \(46~ \text{J}\)
2. \(46~\text{kJ}\)
3. \(23~\text{J}\)
4. \(23~\text{kJ}\)

A balloon filled with helium (\(32^\circ \mathrm{C}\) and \(1.7\) atm) bursts. Immediately afterwards the expansion of helium can be considered as: