Work Done

Q.

0.1 mol of ideal gas compressed reversibly isothermally from 10 l to 1 l at 100 K. The work done in the process is-

Q. A container with a mass of 5 kg is lifted to a height of 8 m. Work done by the gravitational force is equal to

1. 40 J
2. -40 J
3. 400 J
4. -400 J

Q. Work done by $0.1\text{mole}$ of a gas at ${27}^{\circ }\text{C}$ to double its volume at constant pressure is
[Take $R=2{\text{cal mol}}^{-1}{\text{K}}^{-1}$]

1. $54\text{cal}$
2. $600\text{cal}$
3. $60\text{cal}$
4. $546\text{cal}$

Q. One mole of an ideal gas is heated slowly so that it goes from the $P-V$ state $(P_i,V_i)$ to $(3P_i,3V_i)$ in such a way that the pressure of the gas is directly proportional to the volume. How much work is done on the gas in the process?

1. $4P_i{V}_i$
2. $16P_i{V}_i$
3. $-9P_i{V}_i$
4. $-4P_i{V}_i$

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. One $\text{mole}$ of an ideal diatomic gas at $300\text{K}$ is compressed adiabatically to one-fourth of its volume. If $\gamma =1.5$, the work done on gas will be

1. $1280\text{J}$
2. $1610\text{J}$
3. $2044\text{J}$
4. $4986\text{J}$

Q. If heat absorbed by the working substance from the source is $Q_1=550\text{J}$, heat rejected to the sink is $Q_2=200\text{J}$ then work done by the working substance in a cyclic process is

1. $250\text{J}$
   
2. $350\text{J}$
3. $750\text{J}$
4. $550\text{J}$

Q. An ideal monoatomic gas is taken around the cycle $ABCD$ as shown in figure below. Work done during the cycle is

1. $PV$
2. $3PV$
3. $-PV$
4. $0$

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. 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. An ideal gas is taken through a quasi-static process described by $P=\alpha V^2$, with $\alpha =5.00{\text{atm/m}}^6$. The gas is expanded to twice its original volume of $1.00{\text{m}}^3$. How much work is done by the gas (in $\text{MJ}$) during expansion in this process?

Q. In an isothermal reversible expansion, if the volume of $96\text{g}$ of oxygen at ${27}^{\circ }\text{C}$ is increased from $70\text{litres}$ to $140\text{litres}$, then the work done by the gas will be

1. $300R{\log }_{10}2$
2. $2.3\times 900R{\log }_{10}2$
3. $600R{\log }_{10}2$
4. $2.3\times 300R{\log }_{10}2$

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. In an isothermal reversible expansion if the volume of $96\text{g}$ of oxygen at ${27}^{\circ }\text{C}$ is increased from $70\text{L}$ of $140\text{L}$, then the work done by the gas will be

1. $300{\text{R log}}_{10}2$
2. $81{\text{R log}}_{e}2$
3. $900{\text{R log}}_{10}2$
4. $2070{\text{R log}}_{10}2$

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

Q. How much work should be done in decreasing the volume of an ideal gas by an amount of $2.4\times {10}^{-4}{\text{m}}^3$ at normal temperature and constant pressure of $1\times {10}^5{\text{N/m}}^2$ ?

1. $28\text{J}$
2. $27\text{J}$
3. $25\text{J}$
4. $24\text{J}$

Q. A thermodynamic system goes from state (i) $(P,V)$ to $(2P,V)$ and (ii) $(P,V)$ to $(P,2V)$ as shown in the figure. Work done in the two cases is :

1. Zero, Zero
2. Zero, $PV$
3. $PV$, Zero
4. $PV,PV$

Q. Work done for the process A$\to$ B shown in the figure is

1. $1\text{J}$
2. $1.5\text{J}$
3. $4.5\text{J}$
4. $0.3\text{J}$

Q. One $\text{mole}$ of an ideal diatomic gas at $300\text{K}$ is compressed adiabatically to one-fourth of its volume. If $\gamma =1.5$, the work done on gas will be

1. $1280\text{J}$
2. $1610\text{J}$
3. $2044\text{J}$
4. $4986\text{J}$

Q. One mole of an ideal gas is heated slowly so that it goes from the $P-V$ state $(P_i,V_i)$ to $(3P_i,3V_i)$ in such a way that the pressure of the gas is directly proportional to the volume. How much work is done on the gas in the process?

1. $4P_i{V}_i$
2. $16P_i{V}_i$
3. $-9P_i{V}_i$
4. $-4P_i{V}_i$

Q. In figure, certain mass of gas traces three paths $1,2,3$ from state $P$ to state $Q$. If the work done by the gas along three paths are $W_1,W_2,W_3$ respectively, then

1. $W_1<W_2<W_3$
2. $W_1=W_2=W_3$
3. $W_1>W_2>W_3$
4. Data insufficient

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. How much work should be done in decreasing the volume of an ideal gas by an amount of $2.4\times {10}^{-4}{\text{m}}^3$ at normal temperature and constant pressure of $1\times {10}^5{\text{N/m}}^2$ ?

1. $28\text{J}$
2. $27\text{J}$
3. $25\text{J}$
4. $24\text{J}$

Q. $V-T$ diagram for $n$ moles of monoatomic gas is given below:

Choose the correct statement(s).

1. $\left|\frac{\Delta Q_{1-2}}{\Delta Q_{3-4}}\right|=\frac{1}{2}$
2. $\left|\frac{\Delta Q_{1-2}}{\Delta Q_{2-3}}\right|=\frac{5}{3}$
3. Work done in cyclic process is $\Delta W=\frac{nR{T}_0}{2}$
4. There are only adiabatic and isochoric processes

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. A container with a mass of 5 kg is lifted to a height of 8 m. Work done by the gravitational force is equal to

1. 40 J
2. -40 J
3. 400 J
4. -400 J

Q. One mole of an ideal gas is kept enclosed under a light piston of area $A={10}^{-2}{\text{m}}^2$ which is connected to a compressed spring of spring constant $100\text{N/m}$. The volume of the gas is $0.83{\text{m}}^3$ and its temperature is $100\text{K}$. The gas is heated so that it compresses the spring further by $0.1\text{m}$. The work done by the gas in the process is: [Take$R=8.3\text{J/K mol}$ and suppose there is no atmosphere].

1. $3\text{J}$
2. $6\text{J}$
3. $9\text{J}$
4. $1.5\text{J}$

Q. A gas expands with temperature according to the relation $V=k{T}^{2/3}$. What is the work done, when the temperature changes by ${30}^{\circ }\text{C}$?

1. $10R$
2. $20R$
3. $30R$
4. $40R$

Q. $P-V$ diagram of an ideal gas is shown in the figure. Work done by the gas in process $ABCD$ is

1. $4P_0{V}_0$
2. $2P_0{V}_0$
3. $3P_0{V}_0$
4. $P_0{V}_0$

Q. Fig. shows an indicator diagram. During path $1-2-3$, $100\text{cal}$ are given to the system and $40\text{cal}$ worth work is done. During path $1-4-3$, the work done is $10\text{cal}$.

1. Heat given to the system during path $1-4-3$ is $70\text{cal}$
2. If the system is brought from $3$ to $1$ along straight line path $3-1$, work done is worth $25\text{cal}$
3. Along straight line path $3-1$, the heat ejected by the system is $85\text{cal}$
4. The internal energy of the system in state $3$ is $140\text{cal}$ above that in state $1$.