A cyclic process for \(1\) mole of an ideal gas is shown in the \(V\text-T\) diagram. The work done in \(AB, BC\) and \(CA\) respectively is:

           

1.	\(0, R T_2 \ln \left(\frac{V_1}{V_2}\right), R\left(T_1-T_2\right)\)
2.	\(R\left(T_1-T_2\right), 0, R T_1 \ln \frac{V_1}{V_2}\)
3.	\(0, R T_2 \ln \left(\frac{V_2}{V_1}\right), R\left(T_1-T_2\right)\)
4.	\(0, R T_2 \ln \left(\frac{V_2}{V_1}\right), R\left(T_2-T_1\right)\)

The Carnot cycle (reversible) of gas is represented by a pressure-volume curve as shown in the figure. Consider the following statements:

Which of the statement(s) given above is/are correct?

The heat energy absorbed by a system is going through a cyclic process shown in the figure is:

(1) 10⁷ $\pi$ J

(2) 10⁴ $\pi$ J

(3) 10² $\pi$ J

(4) 10^–3$\pi$ J

When a system is taken from state i to a state f along path iaf, Q = 50 J and W = 20 J.

 If W = –13 J for the curved return path fi, Q for this path is -

1. 33 J

2. 23 J

3. – 7 J

4. – 43 J

An ideal gas is taken from point A to the 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

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

Which of the following graphs correctly represents the variation of $\beta =-(dV/dP)/V$ with P for an ideal gas at constant temperature ?

(1)

(2)

(3)

(4)

An ideal monoatomic gas expands in such a manner that its pressure and volume can be related by equation $P{V}^{5/3} = cons\tan t$. During this process, the gas is 

(1) Heated

(2) Cooled

(3) Neither heated nor cooled

(4) First heated and then cooled

When an ideal gas (γ = 5/3) is heated under constant pressure, then what percentage of given heat energy will be utilised in doing external work ?

1. 40 %

2. 30 %

3. 60 %

4. 20 %