At {27^o}C a gas is suddenly compressed such that its pressure becomes frac{1}{8}th of original pres

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11.Thermodynamics

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At ${27^o}C$ a gas is suddenly compressed such that its pressure becomes $\frac{1}{8}th$ of original pressure. Temperature of the gas will be $(\gamma = 5/3)$

$420K$

${327^o}C$

$300K$

$ - {142^o}C$

Solution

(d) ${T^\gamma }{P^{1 – \gamma }} = $constant ==> $T \propto {P^{\frac{{\gamma – 1}}{\gamma }}}$
==> $\frac{{{T_2}}}{{{T_1}}} = {\left( {\frac{{{P_2}}}{{{P_1}}}} \right)^{\frac{{\gamma – 1}}{\gamma }}} = {\left( {\frac{1}{8}} \right)^{\frac{{5/3 – 1}}{{5/3}}}}$
${T_2} = 300 \times {\left( {\frac{1}{8}} \right)^{0.4}} = 131K = – 142^\circ C$

Standard 11

Physics

During the adiabatic expansion of $2 \,moles$ of a gas, the internal energy was found to have decreased by $100 J$. The work done by the gas in this process is ….. $J$

easy

The $PV$ diagram shows four different possible reversible processes performed on a monatomic ideal gas. Process $A$ is isobaric (constant pressure). Process $B$ is isothermal (constant temperature). Process $C$ is adiabatic. Process $D$ is isochoric (constant volume). For which process$(es)$ does the temperature of the gas decrease?

medium

A certain amount of gas of volume $V$ at $27^{o}\,C$ temperature and pressure $2 \times 10^{7} \;Nm ^{-2}$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $\gamma=1.5$ )

medium

(JEE MAIN-2022)

Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure? where, $1 \rightarrow 2$ is adiabatic.

(Graphs are schematic and are not to scale)

medium

(JEE MAIN-2020)

In Column$-I$ process and in Column$-II$ first law of thermodynamics are given. Match them appropriately :

Column$-I$ Column$-II$

$(a)$ Adiabatic $(i)$ $\Delta Q = \Delta U$

$(b)$ Isothermal $(ii)$ $\Delta Q = \Delta W$

$(iii)$ $\Delta U = -\Delta W$

easy

Column$-I$	Column$-II$
$(a)$ Adiabatic	$(i)$ $\Delta Q = \Delta U$
$(b)$ Isothermal	$(ii)$ $\Delta Q = \Delta W$
	$(iii)$ $\Delta U = -\Delta W$

At ${27^o}C$ a gas is suddenly compressed such that its pressure becomes $\frac{1}{8}th$ of original pressure. Temperature of the gas will be $(\gamma = 5/3)$

Solution

Similar Questions

During the adiabatic expansion of $2 \,moles$ of a gas, the internal energy was found to have decreased by $100 J$. The work done by the gas in this process is ….. $J$

A certain amount of gas of volume $V$ at $27^{o}\,C$ temperature and pressure $2 \times 10^{7} \;Nm ^{-2}$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $\gamma=1.5$ )

Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure? where, $1 \rightarrow 2$ is adiabatic. (Graphs are schematic and are not to scale)

In Column$-I$ process and in Column$-II$ first law of thermodynamics are given. Match them appropriately : Column$-I$ Column$-II$ $(a)$ Adiabatic $(i)$ $\Delta Q = \Delta U$ $(b)$ Isothermal $(ii)$ $\Delta Q = \Delta W$ $(iii)$ $\Delta U = -\Delta W$

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Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure? where, $1 \rightarrow 2$ is adiabatic.

(Graphs are schematic and are not to scale)

In Column$-I$ process and in Column$-II$ first law of thermodynamics are given. Match them appropriately :

Column$-I$ Column$-II$

$(a)$ Adiabatic $(i)$ $\Delta Q = \Delta U$

$(b)$ Isothermal $(ii)$ $\Delta Q = \Delta W$

$(iii)$ $\Delta U = -\Delta W$