(B) Only $(B)$ and $(C)$ are correct.$(B)$ The Gibbs free energy equation is $G = H - TS$. At constant $T$,this becomes $\Delta G = \Delta H - T \Delt

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(B) Only $(B)$ and $(C)$ are correct.$(B)$ The Gibbs free energy equation is $G = H - TS$. At constant $T$,this becomes $\Delta G = \Delta H - T \Delta S$.$(C)$ By the definition of entropy change for a reversible process,$dS = \frac{dq_{rev}}{T}$. At constant $T$,this integrates to $\Delta S = \frac{q_{rev}}{T}$.$(A)$ The first law of thermodynamics is $\Delta U = q + w$. For expansion work,$w = -P \Delta V$,so $\Delta U = q - P \Delta V$. Thus,$(A)$ is incorrect.$(D)$ From the enthalpy definition $H = U + PV$,for an ideal gas,$H = U + nRT$. At constant $T$,$\Delta H = \Delta U + \Delta nRT$. Thus,$(D)$ is incorrect.

Class 11 Chemistry Thermodynamics Mix Examples-Thermodynamics and Thermochemistry

Medium

Which of the following relations are correct?
$(A)$ $\Delta U = q + p \Delta V$
$(B)$ $\Delta G = \Delta H - T \Delta S$
$(C)$ $\Delta S = \frac{q_{rev}}{T}$
$(D)$ $\Delta H = \Delta U - \Delta nRT$
Choose the most appropriate answer from the options given below:

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$B$ and $C$ only
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$A$ and $B$ only
D
$B$ and $D$ only

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Mix Examples-Thermodynamics and Thermochemistry

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$28.0 \, L$ of $CO_2$ is produced on complete combustion of $16.8 \, L$ gaseous mixture of ethene $(C_2H_4)$ and methane $(CH_4)$ at $25^{\circ}C$ and $1 \, atm$. Heat evolved during the combustion process is $......... \, kJ$.
Given :
$\Delta H_C(CH_4) = -900 \, kJ \, mol^{-1}$
$\Delta H_C(C_2H_4) = -1400 \, kJ \, mol^{-1}$

DifficultJEE MAIN 2023

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Match the following items in List-$I$ with their corresponding expressions in List-$II$.
List-$I$ List-$II$
$A$. At constant volume the change in internal energy of a system $I$. $W = -2.303 nRT \log \frac{V_f}{V_i}$
$B$. Isothermal irreversible change $II$. $W_{adiabatic} = \Delta U$
$C$. Isothermal reversible change $III$. $q_V = \Delta U$
$D$. Adiabatic change $IV$. $W = -p_{ex} (V_f - V_i)$
$V$. $\Delta U = \Delta H - \Delta nRT$

MediumAP EAMCET 2018

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$36 \, mL$ of pure water takes $100 \, sec$ to evaporate from a vessel and heater connected to an electric source which delivers $806 \, watt$. The $\Delta H_{\text{vaporization}}$ of $H_2O$ is $... \, kJ/mol$

Medium

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The heat associated with the combustion of liquid benzene at constant volume is $-3268 \ kJ \ mol^{-1}$. Calculate the change in enthalpy when this reaction occurs at $300 \ K$ $(R = 8.314 \ J \ K^{-1} \ mol^{-1})$.

Medium

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Calculate the work done during the combustion of $0.138 \ kg$ of ethanol,$(C_2H_5OH_{(l)})$ at $300 \ K$. Given: $R = 8.314 \ J \ K^{-1} \ mol^{-1}$ and molar mass of ethanol $= 46 \ g \ mol^{-1}$. (in $J$)

DifficultMHT CET 2018

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List-$I$	List-$II$
$A$. At constant volume the change in internal energy of a system	$I$. $W = -2.303 nRT \log \frac{V_f}{V_i}$
$B$. Isothermal irreversible change	$II$. $W_{adiabatic} = \Delta U$
$C$. Isothermal reversible change	$III$. $q_V = \Delta U$
$D$. Adiabatic change	$IV$. $W = -p_{ex} (V_f - V_i)$
	$V$. $\Delta U = \Delta H - \Delta nRT$

Which of the following relations are correct?$(A)$ $\Delta U = q + p \Delta V$$(B)$ $\Delta G = \Delta H - T \Delta S$$(C)$ $\Delta S = \frac{q_{rev}}{T}$$(D)$ $\Delta H = \Delta U - \Delta nRT$Choose the most appropriate answer from the options given below:

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$36 \, mL$ of pure water takes $100 \, sec$ to evaporate from a vessel and heater connected to an electric source which delivers $806 \, watt$. The $\Delta H_{\text{vaporization}}$ of $H_2O$ is $... \, kJ/mol$

The heat associated with the combustion of liquid benzene at constant volume is $-3268 \ kJ \ mol^{-1}$. Calculate the change in enthalpy when this reaction occurs at $300 \ K$ $(R = 8.314 \ J \ K^{-1} \ mol^{-1})$.

Calculate the work done during the combustion of $0.138 \ kg$ of ethanol,$(C_2H_5OH_{(l)})$ at $300 \ K$. Given: $R = 8.314 \ J \ K^{-1} \ mol^{-1}$ and molar mass of ethanol $= 46 \ g \ mol^{-1}$. (in $J$)

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Which of the following relations are correct?
$(A)$ $\Delta U = q + p \Delta V$
$(B)$ $\Delta G = \Delta H - T \Delta S$
$(C)$ $\Delta S = \frac{q_{rev}}{T}$
$(D)$ $\Delta H = \Delta U - \Delta nRT$
Choose the most appropriate answer from the options given below: