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JEE Advance - Physics (2017 - Paper 1 Offline - No. 16)

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 of the following options is the only correct representation of a process in which

$$\Delta U = \Delta Q - P\Delta V$$?
$$\left( {{\rm I}{\rm I}} \right)\left( {iv} \right)\left( R \right)$$
$$\left( {{\rm I}{\rm I}{\rm I}} \right)\left( {iii} \right)\left( P \right)$$
$$\left( {{\rm I}{\rm I}} \right)\left( {iii} \right)\left( S \right)$$
$$\left( {{\rm I}{\rm I}} \right)\left( {iii} \right)\left( P \right)$$

Explanation

Compare the given relation, $$\Delta$$U = $$\Delta$$Q $$-$$ p$$\Delta$$V, with the first law of thermodynamics, $$\Delta$$Q = $$\Delta$$U + $$\Delta$$W, to get work done by the gas as $$\Delta$$W = p$$\Delta$$V. This is the work done in an isobaric process. The p-V diagram of this process is shown in (P). The work done in this process is $${W_{1 \to 2}} = \int {pdV = p{V_1} - p{V_2}} $$.

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