Work Done in Reversible Adiabatic Process

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. 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. The equation for work done in a reversible adiabatic expansion can be given by $\frac{nR(T_2-T_1)}{\gamma -1}$.

1. False

2. True

Q. The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the fitgure. 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. $△U_{isothermal}>△U_{adiabatic}$

Q. When $2$ mol of $HCI$ is added to $IL$ of an acidic buffer, its $pH$ changes from $3.4$ to $2.9$. The buffer capacity of the buffer solution is

1. $2$
2. $0$
3. $4$
4. $8$

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. The specific heat of many solids at low temperatures varies with absolute temperature T according to the graph as shown. Then heat energy required to raise the temperature of a unit mass of such a solid from T $=$ 0 to T$=$ 30K is

1. $300\sqrt{3}$ J
2. $900\sqrt{3}$ J
3. $450\sqrt{3}$ J
4. $150\sqrt{3}$ J

Q. The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the fitgure. 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. $△U_{isothermal}>△U_{adiabatic}$

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

1. -8.314 J

2. -16.62 J

3. Unpredictable

4. -4.3 J

Q. When $73$ g of $HCl$ is added to $1L$ of an acidic buffer, its pH changes from $3.4$ to $2.9$. The buffer capacity of the buffer solution is:

1. $7$
2. $8$
3. $9$
4. $4$

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. $\frac{T}{2^{\frac{5}{3}}+1}$

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. $5$ 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. 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. 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. When $73.0$ g of HCl are added to $1$ L of an acidic buffer, its pH changes from $3.4$ to $2.9$. The buffer capacity of the buffer solution is :

Q. 1 mole of $N{H}_3$ gas at $27{}^{o}C$ is expanded in reversible adiabatic condition to make volume 64 times of its initial volume. $(\gamma =\frac{4}{3})$ The magnitude of work done (in cal) will be :
(Give your answer in cal and upto two decimal only)

Q. One gram mol of a diatomic gas $(\gamma =1.4)$ is compressed adiabatically so that its temperature rises from ${27}^{o}C$ to ${127}^{o}C.$ The work done will be

1. 2078.5 joules
2. 207.85 joules
3. 207.85 ergs
4. None of the above

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. 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. Temperature of one mole of a gas is increased by $1^{o}C$ at constant pressure. The work done on the system is:

1. $R$
2. $R/2$
3. $2R$
4. $-R$