Work Done in Reversible Adiabatic Process

Q. 14g oxygen at $0^{\circ }C$ and 10 atm are subjected to reversible adiabatic expansion to a pressure of 1 atm. What is the work done?

1. -12.80 liter atm
2. -11.82 liter atm
3. -11.90 liter atm
4. -12 liter atm

Q. For an adiabatic process, the magnitude of work done by the system or on the system is equal to the change in internal energy of the system.

1. True
2. False

Q. Match the Column - I with Column - II
$\begin{array}{cc}Column-I\left(IdealGas\right)& \text{Column - II (Related equation)}\\ \text{(A) Reversible isothermal process}& \left(P\right)W=-2.303nRTlog\left(V_2/V_1\right)\\ \text{(B) Reversible adiabatic process}& \left(Q\right)W=n{C}_{v,m}(T_2-T_1)\\ \text{(C) Irreversible adiabatic process}& \left(R\right)PV=nRT\\ \text{(D) Irreversible isothermal process}& \left(S\right)W=-{\int }_{v_i}^{v_f}{P}_{ext.}dV\end{array}$

1. $A)P,R,S$
   $B)Q,R,S$
   $C)Q,R,S$
   $D)R,S$
2. $A)P,S$
   $B)Q,S$
   $C)Q,R,S$
   $D)R,S$
3. $A)P$
   $B)Q,S$
   $C)Q,S$
   $D)R,S$
4. $A)P,Q,R,S$
   $B)Q,S$
   $C)Q,S$
   $D)R,S$

Q. An ideal gas at ${27}^{o}C$ is compressed adiabatically and reversibly to $\frac{8}{27}$ of its original volume. If $\gamma =\frac{5}{3},$ then the rise in temperature is

1. $450K$
2. $375K$
3. $225K$
4. $405K$

Q. A system works under cyclic process as follows

Heat absorbed during the process is:

1. $\frac{22}{7}\times {10}^{2}J$
2. $\frac{22}{7}\times {10}^{3}J$
3. $\frac{22}{7}\times {10}^{4}J$
4. $\frac{22}{7}\times {10}^{5}J$

Q. For the process to occur under adiabatic conditions, the correct condition is:

1. $△T=0$
2. $△P=0$
3. $△q=0$
4. $w=0$

Q. $5$ moles of an ideal gas $(C_v=\frac{5}{2}R)$ was compressed adiabatically against a constant pressure of $5atm$, which was initially at $250K$ and $1atm$ pressure. The work done in the process is equal to:

1. 1450 R
2. 3562 R
3. 2500 R
4. 5000 R

Q. 14g oxygen at $0^{\circ }C$ and 10 atm are subjected to reversible adiabatic expansion to a pressure of 1 atm. What is the work done?

1. -12.80 liter atm
2. -11.82 liter atm
3. -11.90 liter atm
4. -12 liter atm

Q. An ideal gas whose adiabatic exponent $\gamma$ is expanded according to the law $P=\alpha V$, where $\alpha$ is a constant. The initial volume of the gas is equal to $V_0$. As a result of expansion, the volume increases $4$ times. Select the correct option for above information.

1. Molar heat capacity of gas in the process is $\frac{R(\gamma +1)}{2(\gamma -1)}$
2. Work done by the gas is $-15V_0^2\frac{\alpha }{2}$
3. Molar heat capacity of gas in the process is $\frac{R(\gamma -1)}{2(\gamma +1)}$
4. Work done by the gas is $+15V_0^2\frac{\alpha }{2}$

Q.

Which of the following is true in case of reversible adiabatic expansion?

1. ${\left(\frac{T_2}{T_1}\right)}^{\gamma }={\left(\frac{P_1}{P_2}\right)}^{\gamma -1}$

2. ${\left(\frac{T_1}{T_2}\right)}^{\gamma }={\left(\frac{P_1}{P_2}\right)}^{\gamma -1}$

3. ${\left(\frac{T_1}{T_2}\right)}^{\gamma }={\left(\frac{P_1}{P_2}\right)}^{1-\gamma }$

4. ${\left(\frac{T_1}{T_2}\right)}^{\gamma }={\left(\frac{P_2}{P_1}\right)}^{1-\gamma }$

Q. One mole ideal monoatomic gas is heated according to path AB and AC. If temperature of state B and C are equal. Calculate $\frac{q_{AC}}{q_{AB}}\times 10$

Q. According to the Arrhenius equation,

1. Rate constant increases with increase in temperature. This is
   due to a greater number of collisions whose energy exceeds
   the activation energy
2. Higher the magnitude of activation energy, stronger is the
   temperature dependence of the rate constant
3. The pre-exponential factor is a measure of the rate at which
   collisions occur, irrespective of their energy
4. A high activation energy usually implies a fast reaction

Q. The reversible expansion of an ideal gas under adiabatic and isothermal condition is shown in the figure. Which of the following statements is incorrect?

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

Q. An ideal monoatomic gas undergoes adiabatic free expansion from $16bar$, $2L$, $300K$ to $16L$.

1. The final pressure of gas becomes zero
2. The final pressure of gas becomes $2bar$
3. The final temperature of gas becomes $300\times {\left(\frac{2}{16}\right)}^{\frac{2}{3}}K$
4. The final temperature of gas becomes $300K$

Q. Work Done in reversible adiabatic process is given by:

1. $2.303RT\log \frac{V_2}{V_1}$
2. $\frac{nR}{(\gamma -1)}(T_2-T_1)$
3. $2.303RT\log \frac{V_1}{V_2}$
4. None of these

Q. One mole of a gas is heated at constant pressure to raise its temperature by $1^{\circ }C$. The work done in joules is

1. $-4.3$
2. $-8.314$
3. $-16.62$
4. Unpredictable

Q. One mole ideal monoatomic gas is heated according to path AB and AC. If temperature of state B and C are equal. Calculate $\frac{q_{AC}}{q_{AB}}\times 10$

Q. When one mole of monoatomic ideal gas at temperature $T$ undergoes adiabatic change reversibly, change in volume is from $1Lto2L$, the final temperature in Kelvin would be

1. $\frac{T}{2^{2/3}}$
2. $T+\frac{2}{3\times 0.0821}$
3. $T$
4. $T-\frac{2}{3\times 0.0821}$

Q. An ideal gas whose adiabatic exponent $\gamma$ is expanded according to the law $P=\alpha V$, where $\alpha$ is a constant. The initial volume of the gas is equal to $V_0$. As a result of expansion, the volume increases $4$ times. Select the correct option for above information.

1. Molar heat capacity of gas in the process is $\frac{R(\gamma +1)}{2(\gamma -1)}$
2. Work done by the gas is $-15V_0^2\frac{\alpha }{2}$
3. Molar heat capacity of gas in the process is $\frac{R(\gamma -1)}{2(\gamma +1)}$
4. Work done by the gas is $+15V_0^2\frac{\alpha }{2}$

Q. A polyatomic gas $(\gamma =\frac{4}{3})$ is compressed to $\frac{1}{8}$ of its volume adiabatically and reversibly. If its initial pressure is $P_0$ its new pressure will be

1. $8P_0$
2. $16P_0$
3. $6P_0$
4. $2P_0$

Q. One mole of an ideal monoatomic gas expands reversibly and adiabatically from a volume of $x$ litre to 14 litre at ${27}^{\circ }C$. Then the value of $x$ will be:[Final temperature $=189\text{K}$ and $C_v=\frac{3}{2}\text{R}$ ]

Q. Five moles of an ideal monoatomic gas at temperature T and volume 2 L expands to 8 L against a constant external pressure of 2 atm under adiabatic conditions. Then the final temperature of the gas will be:

1. $T-\frac{8}{R}$
2. $T-\frac{20}{3R}$
3. $T+\frac{8}{R}$
4. $\frac{T}{2^{\frac{5}{3}}+1}$