List I describes thermodynamic processes in four different systems. List II gives magnitudes (either

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11.Thermodynamics

normal

$List I$ 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?

$I \rightarrow T , II \rightarrow R , III \rightarrow S , IV \rightarrow Q$

$I \rightarrow S , II \rightarrow P , III \rightarrow T , IV \rightarrow P$

$I \rightarrow P, II \rightarrow R , III \rightarrow T , IV \rightarrow Q$

$I \rightarrow Q , II \rightarrow R , III \rightarrow S , IV \rightarrow T$

(IIT-2022)

Solution

$(I)\Delta U =\Delta Q -\Delta W$

$=\left\{\left(10^{-3} \times 2250\right)-\frac{10^5\left(10^{-1}-10^{-4}\right)}{10^5}\right\} VJ$

$=(2.25-0.0999) VJ$

$=(2.1501) kJ$

$(II)$

$\Delta U = nC \Delta T$

$=\frac{5}{2} \pi R_{ T }$

$=\frac{5}{2} \cdot(0.2)(8)(1500-500) J$

$=4 kJ$

$(III)$

$P_1 V_2=P_2 V_2^2$

$\Rightarrow 2\left(\frac{1}{3}\right)^{s, 1}=P_2\left(\frac{1}{24}\right)^s$

$\Rightarrow P_2=64 kPa$

$\Delta U=n C_2 \Delta T=\frac{3}{2} \cdot\left(P_2 V_2-P_1 V_1\right)$

$=\frac{3}{2}\left(64 \times \frac{1}{24}-2 \times \frac{1}{3}\right) kJ$

$=3 VJ$

$(IV)\Delta U = HC C _{ V } \Delta T$

$= n \cdot \frac{7}{2} RAT$

$=\frac{7}{9} \Delta Q$

$=7 kJ$

Standard 11

Physics

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easy

(AIEEE-2005)

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(JEE MAIN-2021)

$List-I$	$List-II$
($I$) $10^{-3} kg$ 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.	($S$) $5 kJ$
	($T$) $3 kJ$

Solution

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