Irreversible Adiabatic Expansion And Compression

Q. An ideal gas having initial pressure P, volume V and temperature T is allowed to expand reversibly and adiabatically until its volume becomes 5.66 V, while its temperature decreases to $\frac{T}{2}$. Work done by the gas during expansion is given by $W=-XPV$. Find the value of $X$. (given $(5.66{)}^{0.4}=2$) Report the answer upto two decimals

Q.

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $\mathrm{\lambda }$ is the ratio of specific heats)

1. $-\mathrm{\gamma }(\mathrm{dV}/\mathrm{V})$

2. $\mathrm{dV}/\mathrm{V}$

3. $1/\mathrm{\gamma }(\mathrm{dV}/\mathrm{V})$

4. $-\mathrm{\gamma }(\mathrm{V}/\mathrm{dV})$

Q. In an adiabatic process, no transfer of heat takes place between system and surroundings. Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following.

1. $△q=0,△T\ne 0,w=0$
2. $△q\ne 0,△T=0,w=0$
3. $△q=0,△T=0,w=0$
4. $△q=0,△T<0,w\ne 0$

Q. The INCORRECT match in the following is :

1. $\Delta G^0<0,K<1$

2. $\Delta G^0<0,K=1$

3. $\Delta G^0>0,K<1$
4. $\Delta G^0<0,K>1$

Q. For an adiabatic free expansion of an ideal gas, which of the following is true?

1. $q=0$, $w=0$, $\Delta U=0$
2. $q=0$, $w=+ve$, $\Delta U=-ve$
3. $q=0$, $w=+ve$, $\Delta U=+ve$
4. $q=+ve$, $w=0$, $\Delta U=-ve$

Q. For an adiabatic, irreversible, free expansion which of the following is/are true

1. $\Delta H=0$
2. $\Delta T=0$
3. $\Delta U=0$
4. $\Delta P_{\mathrm{int}}=0$

Q. One mole of a monoatomic gas at pressure $2\text{atm,}$ $279K$ taken to final pressure $4\text{atm}$ by a reversible path described by $\frac{P}{V}=\text{constant}$. Calculate the magnitude of $\frac{\Delta E}{w}$ for the process.

Q. In a reversible adiabatic expansion of air (assume it a mixture of $N_2$ and $O_2$), the volume increases by $25\%$, then the percentage change in pressure is:
(Take ${0.8}^{1.4}=0.73$)

1. decreases by $35\%$
2. increases by $40\%$
3. increases by $27\%$
4. decreases by $27\%$

Q.

For a free expansion of an ideal gas in an isolated chamber which of the following statements is true?

1. (a) Positive work is done by the system.

2. (b) The entropy of the system increases.

3. (c) The temperature of the system decreases.

4. (d) The internal energy of the system decreases.

Q. $16\text{g}$ oxygen gas expands at STP to occupy double of its original volume. The work done during the process is:

1. $260\text{cal}$
2. $180\text{cal}$
3. $130\text{cal}$
4. $272.8\text{cal}$

Q. The relation between U, p and V for an ideal gas in an adiabatic process is given by relation U = a+ bpV. Find the value of adiabatic exponent $\gamma$ of this gas.

1. $\frac{b+1}{b}$
2. $\frac{b+1}{a}$
3. $\frac{a+1}{b}$
4. $\frac{a}{a+b}$

Q. Which thermodynamic parameter is not a state function?

1. q at constant pressure
2. q at constant volume
3. W at adiabatic
4. W at isothermal

Q. 20 litres of a monoatomic ideal gas at $0^{o}C$ and 20 $atm$ 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 = 165 K, V = 247.5 L
2. T = 169 K, V = 257.5 L
3. T = 169 K, V = 247.5 L
4. none of these

Q. An ideal gas in thermally insulated vessel at internal pressure $=p_1$, volume $=V_1$ and absolute temperature $=T_1$ expands irreversibly against zero external pressure, as shown in the diagram.
The final internal pressure, volume and absolute temperature of the gas are $p_2,V_{2}and{T}_2$ respectively.
For this expansion

1. q = 0
2. $T_2=T_1$
3. $p_2{V}_2=p_1{V}_1$
4. $p_2{V}_2^{\gamma }=p_1{V}_1^{\gamma }$

Q. $\Delta G$ is the net energy available to do useful work and is a measure of free energy. If a reaction has positive enthalpy change and positive entropy change, under what conditions will the reaction be spontaneous?

1. $\Delta G$ will be positive at low temperature hence reaction is spontaneous at low temperature
2. $\Delta G$ is negative at high temperature hence reaction is spontaneous at high temperature
3. $\Delta G$ is negative at low temperatue hence reaction is spontaneous at low temperature
4. $\Delta G$ is negative at all temperatures hence reaction is spontaneous at all temperatures

Q. For the isothermal expansion of an ideal gas into vaccum, the values of $\Delta U=x,q=y,w=z$. Find the value of $x\times y\times z$.

Q. An ideal gas in thermally insulated vessel at internal pressure $=p_1$, volume $=V_1$ and absolute temperature $=T_1$ expands irreversibly against zero external pressure, as shown in the diagram.
The final internal pressure, volume and absolute temperature of the gas are $p_2,V_{2}and{T}_2$ respectively.
For this expansion

1. q = 0
2. $T_2=T_1$
3. $p_2{V}_2=p_1{V}_1$
4. $p_2{V}_2^{\gamma }=p_1{V}_1^{\gamma }$

Q. The standard reaction Gibbs energy for a chemical reaction at an absolute temperature T is given by, ${\Delta }_r{G}^o=A-BT$
Where A and B are non-zero constants.
Which of the following is true about this reaction?

1. Endothermic if, $A<0andB>0$
2. Exothermic if, $B<0$
3. Exothermic if $A>0andB<0$
4. Endothermic if, $A>0$

Q. A process in which pressure remains constant, is called:

1. isothermal process
2. isochoric process
3. adiabatic process
4. isobaric process

Q. One mole of an ideal gas is expanded from a volume of $3L$ to $5L$ under a constant pressure of $1atm$. Calculate the work done by the gas.

Q. For an adiabatic free expansion of an ideal gas, which of the following is true?

1. $q=0$, $w=0$, $\Delta U=0$
2. $q=0$, $w=+ve$, $\Delta U=-ve$
3. $q=0$, $w=+ve$, $\Delta U=+ve$
4. $q=+ve$, $w=0$, $\Delta U=-ve$

Q. The correct statements among the following is/are:

1. PV is a state function
2. Work done under adiabatic condition is a state function
3. Heat at constant volume is a state function
4. Heat at constant pressure is a state function

Q. For an adiabatic, irreversible, free expansion which of the following is/are true

1. $\Delta H=0$
2. $\Delta T=0$
3. $\Delta U=0$
4. $\Delta P_{\mathrm{int}}=0$

Q. Explain first law of Thermodynamics and give its limitations.

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

1. $T=174.9$K, $V=64.0$ liters
2. $T=153$K, $V=57$ liters
3. $T=161.2$K, $V=68.3$ liters
4. $T=165.4$K, $V=78.8$ liters

Q. 20 litres of a monoatomic ideal gas at $0^{o}C$ and 20 $atm$ 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 = 169 K, V = 247.5 L
2. T = 165 K, V = 247.5 L
3. T = 169 K, V = 257.5 L
4. none of these

Q. The correct statements among the following is/are:

1. PV is a state function
2. Work done under adiabatic condition is a state function
3. Heat at constant volume is a state function
4. Heat at constant pressure is a state function

Q. A low pressures, the vander Waal's equation is written as [p+ $\frac{a}{v^2}]$V = RT. The compressibility factor is then equal to :

1. (1 - $\frac{a}{RTV}$)
2. (1 - $\frac{RTV}{a}$)
3. (1 + $\frac{a}{RTV}$)
4. (1 + $\frac{RTV}{a}$)

Q. Match the following

	Column I		Column II
(A)	Standard free energy change	(p)	$nR\ln \frac{V_2}{V_1}$
(B)	Enthalpy change	(q)	$-RT\ln K$
(C)	Entropy change	(r)	$\Delta E+P\Delta V$
(D)	Free energy change	(s)	$-nFE$
		(t)	$\Delta U+\Delta ngRT$