What is the nature of change in internal energy in the following three thermodynamic processes shown in figure?

(1) $∆U$ is  positive in all the three cases

(2) $∆U$ is negative in all the three cases

(3) $∆U$ is positive for (i), negative for (ii), zero for (iii)

(4) $∆U$ = 0, in all the cases

An ideal gas undergoes a cyclic process ABCA as shown. The heat exchange between the system and the surrounding during the process will be:

A cyclic process ABCD is shown in the P-V diagram. Which of the following curves represent the same process?

\(1~\text g\) 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. \(2256~\text J\) 

Which of the following thermodynamic quantities is an outcome of the second law of thermodynamics ?

1. Work

2. Enthalpy

3. Internal energy

4. Entropy

An ideal gas going through the reversible cycle $\mathrm{a}\to \mathrm{b}\to \mathrm{c}\to \mathrm{d}$, has the V-T diagram as shown below in the figure. Process $\mathrm{d}\to \mathrm{a}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>\mathrm{b}\to \mathrm{c}$ are adiabatic.

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

1. 

2. 

3. 

4. 

A and B are two adiabatic curves for two different gases.
Then A and B corresponds to :

1. Ar and He respectively.
2. He and H${}_2$ respectively.
3. O${}_2$ and H${}_2$ respectively.
4. H${}_2$ and He respectively

n moles of an ideal gas is heated at constant pressure
from 50°C to 100°C, the increase in internal energy
of the gas is $\left(\frac{{\mathrm{C}}_{\mathrm{p}}}{{\mathrm{C}}_{\mathrm{v}}}=\mathrm{\gamma }<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>\mathrm{R}=\mathrm{gas}<mspace\; width="1em"></mspace>\mathrm{constant}\right)$

1. $\frac{50<mspace\; width="1em"></mspace>\mathrm{nR}}{\mathrm{\gamma }-1}$

2. $\frac{100<mspace\; width="1em"></mspace>\mathrm{nR}}{\mathrm{\gamma }-1}$

3. $\frac{50<mspace\; width="1em"></mspace>\mathrm{n\gamma R}}{\mathrm{\gamma }-1}$

4. $\frac{25<mspace\; width="1em"></mspace>\mathrm{n\gamma R}}{\mathrm{\gamma }-1}$

A gas mixture consists of 2 moles of ${\mathrm{O}}_2$ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is 

1. 4 RT

2. 15 RT

3. 9 RT

4. 11 RT

The molar heat capacity for an ideal gas

1.  cannot be negative

2.  must be equal to either ${\mathrm{C}}_{\mathrm{V}}$ or ${\mathrm{C}}_{\mathrm{P}}$

3.  must lie in the range ${\mathrm{C}}_{\mathrm{V}}\le \mathrm{C}\le {\mathrm{C}}_{\mathrm{P}}$

4.  may have any value between $-\infty$ and $+\infty$