Work Done

Q. List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.

	List -I		List -II
(I)	${10}^{–3}\text{kg}$ of water at ${100}^{\circ }C$ is converted to steam at the same temperature, at a pressure of ${10}^5\text{Pa}$. The volume of the system changes from ${10}^{–6}$ to ${10}^{–3}$ in the process. Latent heat of water $=2250\text{kJ/kg}$.	(P)	$2\text{kJ}$
(II)	$0.2$ moles of a rigid diatomic ideal gas with volume $V$ at temperature $500\text{K}$ undergoes an isobaric expansion to volume $3V$. Assume $R=8.0{\text{J mol}}^{-1}{K}^{-1}$.	(Q)	$7\text{kJ}$
(III)	One mole of a monoatomic ideal gas is compressed adiabatically from volume $V=\frac{1}{3}{\text{m}}^3$ and pressure $2\text{kPa}$ to volume $\frac{V}{8}$	(R)	$4\text{kJ}$
(IV)	Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9\text{kJ}$ of heat and undergoes isobaric expansion.	(S)	$5\text{kJ}$
		(T)	$3\text{kJ}$

Which one of the following options is correct?

1. $I\to S,II\to P,III\to T,IV\to P$
2. $I\to Q,II\to R,III\to S,IV\to T$
3. $I\to T,II\to R,III\to S,IV\to Q$
4. $I\to P,II\to R,III\to T,IV\to Q$

Q. A cylinder of ideal gas is closed by an $8kg$ movable piston (area $60c{m}^2$). Atmospheric pressure is ${10}^{5}Pa$. When the gas is heated from $30°C$ to $100°C$, the piston rises by $20cm$. The piston is then fixed in its place and the gas is cooled back to $30°C$. Let $\Delta Q_1$ be the heat added to the gas in the heating process and $\left|\Delta Q_2\right|$ the heat lost during cooling. Then the value of $\Delta Q_1-\left|\Delta Q_2\right|$ will be

1. $0$
2. $136J$
3. $-136J$
4. $-68J$

Q. Consider the cyclic process $ABCA$ as shown in the figure, performed on a sample of $2.0$ mole of an ideal gas. A total of $1200\text{J}$ of heat is withdrawn from the sample in the process. Find the magnitude of the work done (in joules) by the gas during the part $BC$. $(R=8.3{\text{JK}}^{-1}{\text{mol}}^{-1})$

1. $2580\text{J}$
2. $3625\text{J}$
3. $4520\text{J}$
4. $1550\text{J}$

Q. The gas inside a spherical bubble expands uniformly and slowly so that its radius increases from $R$ to $2R$. Let the atmospheric pressure be $P_0$ and surface tension be $S$. The work done by the gas in the process is

1. $\frac{28\pi P_0{R}^3}{3}+24\pi S{R}^2$
2. $\frac{25\pi P_0{R}^3}{3}+24\pi S{R}^2$
3. $\frac{28\pi P_0{R}^3}{3}+\frac{23\pi S{R}^2}{2}$
4. none of these

Q. A vertical cylinder piston system has cross-section $S$. It contains $1$ mole of an ideal monatomic gas under a piston of mass $M$. At a certain instant a heater is switched on which transmits heat $q$ per unit time of the cylinder. Assume the piston is in equilibrium at all times during the process. The velocity $v$ of the piston given the condition that pressure under the piston is constant and the system is thermally insulated is $\frac{xq}{5S(P_o+\frac{Mg}{S})}$. Here the value of $x$ is

Q. During an integral number of complete cycles, a reversible engine (shown by a circle) absorbs $1200$ joule from reservoir at $400\text{K}$ and performs $200$ joule of mechanical work.
(a) Find the quantities of heat exchanged with the second reservoir.

(b) Find the change of entropy in second reservoir (in $J/K$).
(c) What is the change in entropy of the universe?

Q. An ideal monoatomic gas is taken around the cycle $ABCDA$ as shown in the $PV$ diagram. The work done during the cycle is given by

1. $\frac{1}{2}PV$
2. $PV$
3. $2PV$
4. $4PV$

Q. An ideal gas is taken through the cycle $A\to B\to C\to A$, as shown in the figure. If the net heat supplied to the gas in the cycle is $5\text{J}$, the work done by the gas in the process $C\to A$ is

1. $-5\text{J}$
2. $-15\text{J}$
3. $-10\text{J}$
4. $-20\text{J}$

Q. Two $\text{moles}$ of an ideal monoatomic gas at ${27}^{\circ }\text{C}$ occupies a volume of $V$. If the gas is expanded adiabatically to the volume $2^{3/2}V$, then the work done by the gas will be $(\gamma =\frac{5}{3},R=8.31\text{J/mol K})$

1. $3739.5\text{J}$
2. $2627.23\text{J}$
3. $2500\text{J}$
4. $-2500\text{J}$

Q. Find the work done by the system in closed path $ABCA$ as shown below.

1. $-\frac{(p_2-p_1)(V_2-V_1)}{2}$
2. $(V_1-V_2)(p_1-P_2)$
3. $\frac{(p_2+p_1)(V_2-V_1)}{2}$
4. Zero