The ratio \(C_P/C_V=1.5\) for a certain ideal gas. The gas is taken at an initial pressure of \(2\) kPa and compressed suddenly to \(\dfrac14\) of its initial volume. The final pressure is:
1. \(\dfrac12\) kPa
2. \(4\) kPa
3. \(8\) kPa
4. \(16\) kPa

The quantity of heat required to take a system from \(\mathrm{A}\) to \(\mathrm{C}\) through the process \(\mathrm{ABC}\) is \(20\) cal. The quantity of heat required to go from \(\mathrm{A}\) to \(\mathrm{C}\) directly is:
    
1. \(20\) cal
2. \(24.2\) cal
3. \(21\) cal
4. \(23\) cal

Refer to figure given below. Let \(ΔU_1\) and \(ΔU_2\) be the change in internal energy in processes \(A\) and \(B\) respectively, \(ΔQ\) be the net heat given to the system in process \(A + B\) and \(ΔW\) be the net work done by the system in the process \( A + B.\)

     
For the above figure:

Choose the correct option from the given ones:

An ideal gas goes from the state \(i\) to the state \(f\) as shown in figure given below. The work done by the gas during the process,

Consider the process on a system shown in the figure. During the process, the work done by the system:
           

If heat is supplied to an ideal gas in an isothermal process,

The first law of thermodynamics is a statement of:
1. conservation of heat
2. conservation of work
3. conservation of momentum
4. conservation of energy