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JEE Advance - Physics (2017 - Paper 1 Offline - No. 17)

An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $$P-V$$ diagram in column 3 of the table. Consider only the path from state $$1$$ to state $$2.$$ $$W$$ denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here $$Y$$ is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is $$n.$$


An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $$P-V$$ diagram in column 3 of the table. Consider only the path from state $$1$$ to state $$2.$$ $$W$$ denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here $$Y$$ is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is $$n.$$


An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $$P-V$$ diagram in column 3 of the table. Consider only the path from state $$1$$ to state $$2.$$ $$W$$ denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here $$Y$$ is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is $$n.$$


Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?
$$\left( {\rm I} \right)\left( {ii} \right)\left( Q \right)$$
$$\left( {{\rm I}V} \right)\left( {ii} \right)\left( R \right)$$
$$\left( {{\rm I}{\rm I}{\rm I}} \right)\left( {iv} \right)\left( R \right)$$
$$\left( {\rm I} \right)\left( {iv} \right)\left( Q \right)$$

Explanation

Adiabatic process is used as a correction in the determination of the speed of sound in an ideal gas. The p-V diagram of this process is shown in (Q). The work done on the gas in an adiabatic process is given by $${W_{1 \to 2}} = {{{p_2}{V_2} - {p_1}{V_1}} \over {\gamma - 1}}$$.

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