Work done in Isothermal Irreversible Process

Q. Match the following
$\begin{array}{cc}ListI& ListII\\ A.\text{Reversible isothermal expansion}& \left(p\right)w=-R{P}_{ext}\frac{[T_2{P}_1-T_1{P}_2]}{P_1{P}_2}\\ B.\text{Irreversible isothermal expansion}& \left(q\right)w=\frac{R}{\gamma -1}[T_2-T_1]\\ C.\text{Reversible adiabatic expansion}& \left(r\right)w=-P_{ext}(V_2-V_1)\\ D.\text{Irreversible adiabatic expansion}& \left(s\right)w=-nRTlog\left(\frac{V_2}{V_1}\right)\end{array}$

1. A - (r), B - (s). C-(q), D - (p)
2. A - (s), B - (r). C-(p), D - (q)
3. A - (s), B - (r). C-(q), D - (p)
4. A - (p), B - (r). C-(q), D - (s)

Q. 10 litres of a monoatomic ideal gas at $0^{o}C$ and 10 $atm$ pressure is suddenly exposed to 1 $atm$ pressure and the gas expands adiabatically against this constant pressure to maximum possible volume. The final temperature and volume of the gas respectively are

1. T = 174.8 K, V = 64 L
2. T = 153 K, V = 57 L
3. T = 165.4 K, V = 78.8 L
4. T = 161.2 K, V = 68.3 L

Q. One mole of a gas is expanded from ($1L,10atm,300K$) to ($4L,5atm,300K$) against a constant external pressure of $1atm$. The heat capacity of gas is $50J{/}^{o}C.$Then the work done during the process is:
(Take $1Latm\simeq 100J$)

1. $-300J$
2. $-600J$
3. $300J$
4. $-100J$

Q.

One mole of an ideal gas at ${25}^{\circ }C$ expands in volume from 1.0 L to 4.0 L at constant temperature. What work (in J) is done if the gas expands against vacuum ?

1. $-4.0\times {10}^2$

2. $-3.0\times {10}^2$

3. $4.0\times {10}^{2}J$

4. $0J$

Q. Calculate the work done when $5$ moles of oxygen gas contracts isothermally from $85L$ to $15L$ against a constant pressure of $2atm$ at ${25}^{0}C$.

1. $70Latm$
2. $14.0Latm$
3. $140Latm$
4. $7.0Latm$

Q. Match the following
$\begin{array}{cc}ListI& ListII\\ A.\text{Reversible isothermal expansion}& \left(p\right)w=-R{P}_{ext}\frac{[T_2{P}_1-T_1{P}_2]}{P_1{P}_2}\\ B.\text{Irreversible isothermal expansion}& \left(q\right)w=\frac{R}{\gamma -1}[T_2-T_1]\\ C.\text{Reversible adiabatic expansion}& \left(r\right)w=-P_{ext}(V_2-V_1)\\ D.\text{Irreversible adiabatic expansion}& \left(s\right)w=-nRTlog\left(\frac{V_2}{V_1}\right)\end{array}$

1. A - (r), B - (s). C-(q), D - (p)
2. A - (s), B - (r). C-(p), D - (q)
3. A - (s), B - (r). C-(q), D - (p)
4. A - (p), B - (r). C-(q), D - (s)

Q. If a gas at $10atm$ and $300K$ expands against a constant external pressure of $2atm$ from a volume of 10 litres to 20 litres, the amount of work done is:
Given: 1 L.atm = 101.3 J

1. $17$L.atm
2. $10$ L.atm
3. $-2026$J
4. $2026J$

Q. The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is/are correct?

1. $T_1=T_2$
2. $T_3>T_1$
3. $W_{isothermal}>W_{adiabatic}$
4. $\Delta U_{isothermal}>\Delta U_{adiabatic}$

Q. Find the work done when $5$ moles of hydrogen contracts isothermally from $15$ L to $5$ L against a constant pressure of 1 atm at ${25}^{0}C$.

1. $685.3cal$
2. $-848.2cal$
3. $422.5cal$
4. $-240.5cal$

Q. In a constant volume calorimeter, 3.5 g of a gas with molecular weight 28 was burnt in excess oxygen at 298.0 K. The temperature of the calorimeter was found to increase from 298.0 K to 298.45 K due to the combustion process. Given that the heat capacity of the calorimeter is $2.5kJ{K}^{-1},$ find the numerical value for the enthalpy of combustion of the gas in $kJmo{l}^{-1}.$

1. 9
2. 5
3. 3
4. 2

Q. If a gas at $5atm$ and $373K$ expands against a constant external pressure of $1atm$ from a volume of 2 litres to 10 litres, the amount of work done is:
(Given: $1L.atm=101.3J$)

1. $-402J$
2. $-525.3J$
3. $-212.8J$
4. $-810.4J$