A gas undergoes an isothermal process. The specific heat capacity of the gas in the process is:

An ideal gas undergoes a thermodynamic process described by the equation:
\(PV^2=C,\)
where \(C\) is a constant. The gas transitions from an initial state \((P_1, V_1, T_1)\) to a final state \((P_2, V_2, T_2).\) Which of the following statements is correct?

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 efficiency of a Carnot engine depends upon:

1. the temperature of the sink only.

2. the temperatures of the source and the sink.

3. the volume of the cylinder of the engine.

4. the temperature of the source only.

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. \(2256~\text J\)