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

Q.

A gas is allowed to expand in a well insulated container against constant external pressure of $2.5\mathrm{atm}$ from an initial volume of $2.50\mathrm{L}$ to a final volume of $4.50\mathrm{L}$. The change in internal energy $\mathrm{\Delta }\mathrm{U}$ of the gas in joules will be ?

1. $+505\mathrm{J}$

2. $+1136.25\mathrm{J}$

3. $-500\mathrm{J}$

4. $-505\mathrm{J}$

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

1. 250 R
2. 300 R
3. 380 R
4. 500 R

Q. $10L$ of a monoatomic ideal gas at $0^{o}C$ and $5atm$ is suddenly released to $1atm$ pressure and the gas is expanded adiabatically against the constant pressure. Find the final volume $\left(inL\right)$ of the gas.

1. $54L$
2. $10L$
3. $34L$
4. $74L$

Q.

In the mixture 2 mole of $\mathrm{He}$ and 1 mole of $\mathrm{Ar}$ is present. Find $[{\left({\mathrm{V}}_{\mathrm{RMS}}\right)}_{\mathrm{He}}/{\left({\mathrm{V}}_{\mathrm{RMS}}\right)}_{\mathrm{Ar}}]$at 300 K.

1. 6.32

2. 1.58

3. 3.16

4. 10

Q. When 1 mole of a mono atomic ideal gas a T K undergoes an adiabatic change under a constant external pressure of 1 atm, its volume changes from 1L to 2L. The final temperature in Kelvin is:

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. $2m^3$ volume of a gas ($\gamma =1.4$) at a pressure of $4\times {10}^{5}N/m^2$ is compressed adiabatically so that its volume becomes $0.5m^3$. Calculate the work done in process? (Given $4^{1.4}=6.9$)

1. $1.48\times {10}^{6}J$
2. $4.5\times {10}^{6}J$
3. $3.28\times {10}^{8}J$
4. $4.28\times {10}^{7}J$

Q. 20 litres of a monoatomic 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 volume of the gas respectively are

1. $V=164L$
2. $V=57L$
3. $V=123.7L$
4. $V=68.3L$

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

1. 250 R
2. 300 R
3. 380 R
4. 500 R

Q. P-V plots for two gases during adibatic processes are shown in the following figure. Plots 1 and 2 should correspond respectively to:

1. $He$ and $O_2$
2. $O_2$ and $He$
3. $He$ and $Ar$
4. $O_2$ and $N_2$

Q. A gas $(C_{v,m}=\frac{5}{2}R)$ behaving ideally was allowed to expand reversibly and adiabatically from $1litre$ to $32litre$. It's initial temperature was ${327}^{o}C.$ The molar enthalpy change (in $Jmol{e}^{-1}$) for the process is

1. $-1125R$
2. $-575R$
3. $-1575R$
4. None of these

Q. p-V plots for two gases during adiabatic processes are shown in the following figure. Plots 1 and 2 should correspond respectively to

1. $Heand{O}_2$
2. $O_{2}andHe$
3. $HeandAr$
4. $O_{2}and{N}_2$

Q. For a reversible adiabatic ideal gas expansion, the value of $\frac{dP}{P}$ 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. $10L$ of a monoatomic ideal gas at $0^{o}C$ and $5atm$ is suddenly released to $1atm$ pressure and the gas is expanded adiabatically against the constant pressure. Find the final volume $\left(inL\right)$ of the gas.

1. $54L$
2. $10L$
3. $34L$
4. $74L$

Q. 20 litres of a monoatomic 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 volume of the gas respectively are

1. $V=164L$
2. $V=57L$
3. $V=123.7L$
4. $V=68.3L$

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. The incorrect figure(s) representing isothermal and adiabatic expansion of an ideal gas from a particular initial state is(are):

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

Q. P-V plots for two gases during adibatic processes are shown in the following figure. Plots 1 and 2 should correspond respectively to:

1. $He$ and $O_2$
2. $O_2$ and $He$
3. $He$ and $Ar$
4. $O_2$ and $N_2$

Q. $10L$ of a monoatomic ideal gas at $0^{o}C$ and $5atm$ is suddenly released to $1atm$ pressure and the gas is expanded adiabatically against the constant pressure. Find the final volume $\left(inL\right)$ of the gas.

1. $54L$
2. $10L$
3. $34L$
4. $74L$

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. When 1 mole of a mono atomic ideal gas a T K undergoes an adiabatic change under a constant external pressure of 1 atm, its volume changes from 1L to 2L. The final temperature in Kelvin is:

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