An ideal gas is taken from point A to point B, as shown in the P-V diagram. The work done in the process is:

       
1. $(P_A-P_B)(V_B-V_A)$
2. $\frac{1}{2}(P_B-P_A)(V_B+V_A)$
3. $\frac{1}{2}(P_B-P_A)(V_B-V_A)$
4. $\frac{1}{2}(P_B+P_A)(V_B-V_A)$

Consider a process shown in the figure. During this process the work done by the system -

(1) Continuously increases

(2) Continuously decreases

(3) First increases, then decreases

(4) First decreases, then increases

Six moles of an ideal gas perform a cycle shown in figure. If the temperature are T_A = 600 K, T_B = 800 K, T_C = 2200 K and T_D = 1200 K, the work done per cycle is -

(1) 20 kJ

(2) 30 kJ

(3) 40 kJ

(4) 60 kJ

In the following figure, four curves A, B, C and D are shown. The curves are 

(1) Isothermal for A and D while adiabatic for B and C

(2) Adiabatic for A and C while isothermal for B and D

(3) Isothermal for A and B while adiabatic for C and D

(4) Isothermal for A and C while adiabatic for B and D

P-V diagram of a cyclic process ABCA is as shown in figure. Choose the correct statement

(1) $\Delta Q_{A\to B}$ = negative

(2) $\Delta U_{B\to C}$ = positive

(3) $\Delta W_{CAB}$ = negative

(4) All of these

In the following P-V diagram two adiabatics cut two isothermals at temperatures T₁ and T₂ (fig.). The value of $\frac{V_a}{V_d}$ will be

(1) $\frac{V_b}{V_c}$

(2) $\frac{V_c}{V_b}$

(3) $\frac{V_d}{V_a}$

(4) V_bV_c

An ideal gas with adiabatic exponent $\left(\mathrm{\gamma }=1.5\right)$ undergoes a process in which work done by the gas is same as increase in internal energy of the gas. The molar heat capacity of gas for the process is –

1. $\mathrm{C}=4\mathrm{R}$

2. $\mathrm{C}=0$

3. $\mathrm{C}=2\mathrm{R}$

4. $\mathrm{C}=\mathrm{R}$

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. ${\mathrm{C}}_{\mathrm{V}} + \mathrm{R}$ 

2. ${\mathrm{C}}_{\mathrm{V}} – \mathrm{R}$ 

3. ${\mathrm{C}}_{\mathrm{V}} + 2\mathrm{R}$

4. ${\mathrm{C}}_{\mathrm{V}} – 3\mathrm{R}$

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  $\mathrm{\gamma }= {\mathrm{C}}_{\mathrm{P}}/{\mathrm{C}}_{\mathrm{V}}$ , the work done by one mole of gas during heating from ${\mathrm{T}}_0$ to $\mathrm{\eta } {\mathrm{T}}_0$ through the given process will be:

1.  $\frac{1}{\mathrm{a}} \ln \mathrm{\eta }$

2.  $\mathrm{a} \ln \mathrm{\eta }- \left(\frac{\mathrm{\eta }-1}{\mathrm{\gamma }-1}\right) {\mathrm{RT}}_0$

3.  $\mathrm{a} \ln \mathrm{\eta }-\left(\mathrm{\gamma }-\mathrm{A}\right) {\mathrm{RT}}_0$

4.  none of these