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A system goes from $P$ to $Q$ by two different paths in the $P - V$ diagram as shown in figure. Heat given to the system in path $1$ is $1000\,J$ . The work done by the system along path $1$ is more than path $2$ by $100\,J$ . What is the heat exchanged by the system in path $2$ ?
Solution
For path $1:$ Heat given $Q_{1}=+1000 \mathrm{~J}$ Work done $=W_{1}$
For path $2:$ Work done $W_{2}=W_{1}-100 \mathrm{~J}$
Heat given $Q_{2}=?$
As change in internal energy between two states for different path is same.
$\therefore \Delta U=Q_{1}-W_{1}=Q_{2}-W_{2}$
$\therefore 1000-W_{1}=Q_{2}-\left(W_{1}-100\right)$
$\therefore Q_{2}=1000-W_{1}+W_{1}-100$
$\therefore Q_{2}=900 \mathrm{~J}$
Similar Questions
$List I$ describes thermodynamic processes in four different systems. $List II$ gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.
| $List-I$ | $List-II$ |
| ($I$) $10^{-3} kg$ of water at $100^{\circ} C$ is converted to steam at the same temperature, at a pressure of $10^5 Pa$. The volume of the system changes from $10^{-6} m ^3$ to $10^{-3} m ^3$ in the process. Latent heat of water $=2250 kJ / kg$. | ($P$) $2 kJ$ |
| ($II$) $0.2$ moles of a rigid diatomic ideal gas with volume $V$ at temperature $500 K$ undergoes an isobaric expansion to volume $3 V$. Assume $R=8.0 Jmol ^1 K^{-1}$. | ($Q$) $7 kJ$ |
| ($III$) On mole of a monatomic ideal gas is compressed adiabatically from volume $V=\frac{1}{3} m^3$ and pressure $2 kPa$ to volume $\frac{v}{8}$ | ($R$) $4 kJ$ |
| ($IV$) Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9 kJ$ of heat and undergoes isobaric expansion. | ($S$) $5 kJ$ |
| ($T$) $3 kJ$ |
Which one of the following options is correct?
