Work done in Isothermal Irreversible Process

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 X 10²

2. 4.0 X 10² J

3. 0 J

4. - 3.0 X10²

Q. Work done on the gas, W, in an irreversible expansion is given by $W=-P_{ext}\times dV$, where $P_{ext}$ is the external pressure and dV is the change in volume of the gas (i.e., $V_{final}-V_{initial}$). What is the value of work done on 1 mole of an ideal gas when it expands into vaccum?

1. 2.27 J
2. Infinite
3. 0 J
4. 8.314 KJ

Q. Under isothermal conditions, a gas at 300 K expands from 0.1 L to 0.25 L against a constant external pressure of 2 bar. The work done by the gas is:
(Given that 1 L bar = 100 J)

1. 5 kJ
2. 25 J
3. 30 J
4. -30 J

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 = 165.4 K, V = 78.8 L
3. T = 153 K, V = 57 L
4. T = 161.2 K, V = 68.3 L

Q. Two mole of ideal diatomic gas $(C_{v,m}=5/2R)$ at $300K$ and $5atm$ expanded irreversibly and adiabatically to a final pressure of $2atm$ against a constant pressure of 1 atm. Calculate change in internal energy $△U$

1. $864.28J$
2. $-1052.1J$
3. $-1247.1J$
4. $-2164.1J$

Q. Match the following
$\begin{array}{cc}ListI& ListII\\ A.\text{Reversible isothermal expansion}& \left(p\right)w=-R{P}_{ext}\frac{[T_2{P}_1-T_1{P}_2]}{P_1{P}_2}\\ B.\text{Irreversible isothermal expansion}& \left(q\right)w=\frac{R}{\gamma -1}[T_2-T_1]\\ C.\text{Reversible adiabatic expansion}& \left(r\right)w=-P_{ext}(V_2-V_1)\\ D.\text{Irreversible adiabatic expansion}& \left(s\right)w=-2.303nRTlo{g}_{10}{V}_2/V_1\end{array}$

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

Q. Two identical samples of a gas are allowed to expand (i) isothermally (ii) adiabatically. The magnitude of work done is

1. More in the isothermal process
2. More in the adiabatic process
3. Equal in both processes
4. Dependent on atomicity of gas

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. $2026J$
4. $-2026$J

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

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