Two moles of an ideal monoatomic gas occupies a volume V at 27^o C. The gas expands adiabatically to a volume 2 V. Calculate (a)

Q: Two moles of an ideal monoatomic gas occupies a volume $V$ at $27^o C$. The gas expands adiabatically to a volume $2\ V$. Calculate $(a)$ the final temperature of the gas and $(b)$ change in its internal energy.

b In an adiabatic process $T{V^{\gamma - 1}}=constant$ or ${T_1}{V_1}^{\gamma - 1} = {T_2}{V_2}^{\gamma - 1}$ For monoatomic gas $\gamma = \frac{5}{3}$ $\left( {300} \right){V^{2/3}} = {T_2}{\left( {2V} \right)^{2/3}} \Rightarrow {T_2} = \frac{{300}}{{{{\left( 2 \right)}^{2/3}}}}$ ${T_2} = 189\,K\,\left( {final\,temperature} \right)$ Change in internal energy $\Delta U = n\frac{f}{2}R\,\Delta T$ $ = 2\left( {\frac{3}{2}} \right)\left( {\frac{{25}}{3}} \right)\left( { - 111} \right) = - 2.7\,kJ$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

Two moles of an ideal monoatomic gas occupies a volume $V$ at $27^o C$. The gas expands adiabatically to a volume $2\ V$. Calculate $(a)$ the final temperature of the gas and $(b)$ change in its internal energy.

A$(a)$ $195 $ $K$ $(b)$ $-2.7$ $kJ$
B$(a)$ $189$ $K$ $(b)$ $-2.7$ $kJ$
C$(a)$ $195$ $K$ $(b)$ $2.7$ $kJ$
D$(a)$ $189$ $ K$ $(b)$ $2.7$ $kJ$

JEE MAIN 2018, Medium

STD 11 Science
NEET
STD 11 - 11. thermodynamics
Physics

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Download App

Similar Questions

1
A total of $48 \mathrm{~J}$ heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $2^{\circ} \mathrm{C}$. The work done by the gas is : (Given, $\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$.)
View Solution
2
A gas can be taken from $A$ to $B$ via two different processes $ACB$ and $ADB$. When path $ACB$ is used $60\, J$ of heat flows into the system and $30\, J$ of work is done by the system. If path $ADB$ is used work down by the system is $10\, J$. the heat flow into the system in path $ADB$ is ..... $J$
View Solution
3
The coefficient of performance of a Carnot refrigerator working between ${30^o}C$ and ${0^o}C$ is
View Solution
4
Volume versus temperature graph of two moles of helium gas is as shown in figure. The ratio of heat absorbed and the work done by the gas in process $1-2$ is
View Solution
5
If a system undergoes contraction of volume then the work done by the system will be
View Solution
6
An ideal gas, initially in state $\left( P _{12}, V _1, T _1\right)$ is expanded isobarically to $\left( P _{12}, V _2, T _2\right)$, then adiabatically $\left( P _{34}, V _3, T _3\right)$. It is then contracted isobarically to $\left( P _{34}, V _4, T _4\right)$ and finally adiabatically back to the initial state. The efficiency of this cycle is
View Solution
7
Heat energy of $735\,J$ is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be $..........\,J$
View Solution
8
For a reversible process, necessary condition is
View Solution
9
Which of the following is incorrect regarding the first law of thermodynamics
View Solution
10
Following figure shows two processes $A$ and $B$ for a gas. If $\Delta Q_A$ and $\Delta Q_B$ are the amount of heat absorbed by the system in two cases, and $\Delta U_A$ and $\Delta U_B$ are changes in internal energies, respectively, then
View Solution

Download our appand get started for free

Similar Questions

Download our app
and get started for free