Two cylinders \(A\) and \(B\) of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. \(B\) is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is: 
1. adiabatic 
2. isochoric 
3. isobaric 
4. isothermal 

The \((P\text{-}V)\) diagram for an ideal gas in a piston-cylinder assembly undergoing a thermodynamic process is shown in the figure. The process is:

\(1~\text g\) of water of volume \(1~\text{cm}^3\) at \(100^\circ \text{C}\) is converted into steam at the same temperature under normal atmospheric pressure \(\approx 1\times10^{5}~\text{Pa}.\) The volume of  steam formed equals \(1671~\text{cm}^3.\) If the specific latent heat of vaporization of water is \(2256~\text{J/g},\) the change in internal energy is:
1. \(2423~\text J\) 
2. \(2089~\text J\) 
3. \(167~\text J\) 
4. \(2256~\text J\) 

An ideal gas goes from state \(A\) to state \(B\) via three different processes as indicated in the \((P\text-V)\) diagram.

  
If \(Q_1,Q_2,Q_3\)${\mathrm{}}_{}$ indicate the heat absorbed by the gas along the three processes and \(\Delta U_1, \Delta U_2, \Delta U_3\) indicate the change in internal energy along the three processes respectively, then:

At a pressure of \(2\) atmospheres, a mass of diatomic gas \((\gamma = 1.4)\), is compressed adiabatically, causing its temperature to rise from \(27^{\circ}\mathrm{C}\) to \(927^{\circ}\mathrm{C}\). The pressure of the gas in the final state is:
1. 8 atm
2. 28 atm
3. 68.7 atm
4. 256 atm

A monoatomic gas at pressure P₁ and volume V₁ is compressed adiabatically to 1/8th its original volume. What is the final pressure of the gas?

1. P₁

2. 16 P₁

3. 32 P₁

4. 64 P₁

Which one of the following processes is reversible?

An ideal gas heat engine operates in a Carnot cycle between 227ºC and 127ºC. It absorbs 6 × 10⁴ cals of heat at higher temperatures. The amount of heat converted to work will be?
1. 4.8 × 10⁴ cals
2. 2.4 × 10⁴ cals
3. 1.2 × 10⁴ cals
4. 6 × 10⁴ cals

When volume changes from \(V\) to \(2V\) at constant pressure(\(P\)), the change in internal energy will be:
1. \(PV\)
2. \(3PV\)
3. \(\frac{PV}{\gamma -1}\)
4. \(\frac{RV}{\gamma -1}\)