Relation between P, V, T, Gamma in Adiabatic Proceses

Q. For a reversible adiabatic ideal gas expansion $\frac{dP}{P}$ is equal to:

1. $\gamma \frac{dV}{V}$
2. $-\gamma \frac{dV}{V}$
3. $\left(\frac{\gamma }{\gamma -1}\right)\frac{dV}{V}$
4. $\frac{dV}{V}$

Q. The work done in adiabatic compression of 2 mole of an ideal monoatomic gas by constant external pressure of 2 atm starting from initial pressure of 1 atm and initial temperature of 300K is:
(Take $R=2cal/K.mol$)

1. 360 cal
2. 720 cal
3. 800 cal
4. 550 cal

Q. An ideal gas in thermally insulated vessel at internal pressure $=P_1$. volume $=V_1$ and absolute temperature $=T_1$ expands irrversibly 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. If one mole of a monatomic gas $(\gamma =\frac{5}{3})$ is mixed with one mole of a diatomic gas $(\gamma =\frac{7}{5})$ the value of $\gamma$ for the mixture is:

Q. An ideal gas in thermally insulated vessel at internal pressure $=P_1$. volume $=V_1$ and absolute temperature $=T_1$ expands irrversibly 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. Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $u=\frac{U}{V}\propto T^4$ and pressure $P=\frac{1}{3}\left(\frac{U}{V}\right)$. If the shell now undergoes an adiabatic expansion the relation between T and R is:

1. $T\propto \frac{1}{R}$
2. $T\propto \frac{1}{R^3}$
3. $T\propto e^{-R}$
4. $T\propto e^{-3R}$

Q. An ideal gas in a 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 which of the following relation(s) holds true?

1. $q=0$
2. $T_2=T_1$
3. $P_2{V}_2=P_1{V}_1$
4. $P_2{V}_2^{\gamma }$

Q. When one mole of monoatomic ideal gas at temperature $T$ undergoes adiabatic change reversibly, change in volume is from $1Lto5L$, the final temperature in Kelvin would be:

1. $\frac{T}{5^{2/3}}$
2. $T+\frac{2}{3\times 0.0821}$
3. $T$
4. $T-\frac{2}{3\times 0.0821}$

Q. The correct figure representing isothermal and adiabatic expansion of an ideal gas from a particular initial state is:

1. A
2. B
3. C
4. D

Q. Two moles of an ideal gas $\left(C_v=\frac{5}{2}R\right)$ was compressed adiabatically against constant pressure of $2atm$, which was initially at $350K$ and $1atm$ pressure. The work involve in the process is equal to?

1. $250R$
2. $300R$
3. $400R$
4. $500R$

Q. Which are true for reversible adiabatic process :

1. $w=2.303RT\log \frac{V_2}{V_1}$
2. $w=\frac{nR}{(\gamma -1)}(T_2-T_1)$
3. $w=2.303RT\log \frac{V_1}{V_2}$
4. $\Delta U=w$ = $n{C}_v\Delta T$

Q. One mol of an ideal gas is allowed to expand reversibly and adiabatically from a temperature of ${27}^{o}C$. If the work done by gas during the process is 2 kJ, then the final temperature of gas is:
Given: $C_v$ for the gas = $20J/K/mol$

1. 100 K
2. 200 K
3. 195 K
4. 255 K

Q. 1 mole of $N{H}_3$ gas at ${27}^{o}C$ is expanded in reversible adiabatic condition to make volume 8 times $(\gamma =1.33).$ Final temperature and magnitude of work done respectively are

1. 150 K, 900 cal
2. 150 K, 400 cal
3. 250 K, 1000 cal
4. 200 K, 800 cal

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