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

1. Work

2. Enthalpy

3. Internal energy

4. Entropy

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 $+\infty$

An ideal gas expands according to the law ${\mathrm{PV}}^2$ = const. The molar heat capacity C is : 

1. ${\mathrm{C}}_{\mathrm{V}}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\mathrm{R}$ 

2. ${\mathrm{C}}_{\mathrm{V}}<mspace\; width="1em"></mspace>–<mspace\; width="1em"></mspace>\mathrm{R}$ 

3. ${\mathrm{C}}_{\mathrm{V}}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>2\mathrm{R}$

4. ${\mathrm{C}}_{\mathrm{V}}<mspace\; width="1em"></mspace>–<mspace\; width="1em"></mspace>3\mathrm{R}$

The molar heat capacity C for an ideal gas going through a given process is given by C = a/T , where 'a' is a constant. If  $\mathrm{\gamma }=<mspace\; width="1em"></mspace>{\mathrm{C}}_{\mathrm{P}}/{\mathrm{C}}_{\mathrm{V}}$ , the work done by one mole of gas during heating from ${\mathrm{T}}_0$ to $\mathrm{\eta }<mspace\; width="1em"></mspace>{\mathrm{T}}_0$ through the given process will be:

1.  $\frac{1}{\mathrm{a}}<mspace\; width="1em"></mspace>\ln <mspace\; width="1em"></mspace>\mathrm{\eta }$

2.  $\mathrm{a}<mspace\; width="1em"></mspace>\ln <mspace\; width="1em"></mspace>\mathrm{\eta }-<mspace\; width="1em"></mspace>\left(\frac{\mathrm{\eta }-1}{\mathrm{\gamma }-1}\right)<mspace\; width="1em"></mspace>{\mathrm{RT}}_0$

3.  $\mathrm{a}<mspace\; width="1em"></mspace>\ln <mspace\; width="1em"></mspace>\mathrm{\eta }-\left(\mathrm{\gamma }-\mathrm{A}\right)<mspace\; width="1em"></mspace>{\mathrm{RT}}_0$

4.  none of these

The pressure of a monoatomic gas increases linearly from $4\times {10}^5$ N/m² to $8\times {10}^5$ N/m² when its volume increases from 0.2 m³ to 0.5 m³. The molar heat capacity of the gas is:
[R = 8.31 J/mol k]  

1. 20.1 J/molK               

2. 17.14 J/molK

3. 18.14 J/molK                                   

4. 20.14 J/molK

\(1~\text g\) 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:

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

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

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