36. (AIEEE 2009 )

Two moles of helium gas are taken over the cycle $A B C D$ , as shown in the $P$ - $T$ diagram. AIEEE 2009 Physics - Heat and Thermodynamics Question 302 English

The net work done on the gas in the cycle $A B C D A$ is:

(A) $276$ $R$

(B) $1076$ $R$

(C) $1904$ $R$

(D) zero

Correct answer is (A)

The net work in the cycle $A B C D$ is
$W = W_{A B} + W_{B C} + W_{C D} + W_{D A}$
$= 400 R + 2.303 n R T \log \frac{P_{B}}{P_{C}} + (- 400 R) - 414 R$
$= 2.303 \times 2 R \times 500 \log \frac{2 \times 10^{5}}{1 \times 10^{5}} - 414 R$
$= 693.2 R - 414 R = 279.2 R$

37. (AIEEE 2007 )

When a system is taken from state $i$ to state $f$ along the path iaf, it is found that $Q = 50$ cal and $W = 20$ $c a l$ . Along the path $i b f$ $Q = 36$ $c a l .$ $W$ along the path $i b f$ is AIEEE 2007 Physics - Heat and Thermodynamics Question 307 English

(A) $14$ $c a l$

(B) $6$ $c a l$

(C) $16$ $c a l$

(D) $66$ $c a l$

Correct answer is (B)

For path iaf, $Δ U = Q - W = 50 - 20 = 30 c a l .$
For path ibf, $W = Q - Δ U = 36 - 30 = 6 c a l .$

38. (AIEEE 2006 )

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $T_{0},$ while Box contains one mole of helium at temperature $(\frac{7}{3}) T_{0} .$ The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases, $T_{f}$ in terms of $T_{0}$ is

(A) $T_{f} = \frac{3}{7} T_{0}$

(B) $T_{f} = \frac{7}{3} T_{0}$

(C) $T_{f} = \frac{3}{2} T_{0}$

(D) $T_{f} = \frac{5}{2} T_{0}$

Correct answer is (C)

Heat lost by He $=$ Heat gained by $N_{2}$
$n_{1} C v_{1} Δ T_{1} = n_{2} C v_{2} Δ T_{2}$
$\frac{3}{2} R [\frac{7}{3} T_{0} - T_{f}]$
$= \frac{5}{2} R [T_{f} - T_{0}] \Rightarrow T_{f}$
$= \frac{3}{2} T_{0}$

39. (AIEEE 2005 )

A system goes from $A$ to $B$ via two processes $I$ and $I I$ as shown in figure. If $Δ U_{1}$ and $Δ U_{2}$ are the changes in internal energies in the processes $I$ and $I I$ respectively, then AIEEE 2005 Physics - Heat and Thermodynamics Question 309 English

(A) relation between $Δ U_{1}$ and $Δ U_{2}$ can not be determined

(B) $Δ U_{1} = Δ U_{2}$

(C) $Δ U_{2} < Δ U_{1}$

(D) $Δ U_{2} > Δ U_{1}$

Correct answer is (B)

Change in internal energy do not depend upon the path followed by the process. It only depends on initial and final states $i . e .,$ $Δ U_{1} = Δ U_{2}$

40. (AIEEE 2003 )

Which of the following parameters does not characterize the thermodynamic state of mattter?

(A) Temperature

(B) Pressure

(C) Work

(D) Volume

Correct answer is (C)

Work is a path function. The remaining three parameters are state function.