(B) For an ideal gas,the change in internal energy is given by $\Delta U = n \times C_v \times \Delta T$. Given $n = 5 \, mol$,$C_v = 28 \, J \, K^{-1

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$\Delta U = 14 \, kJ ; \Delta (pV) = 4 \, kJ$

(B) For an ideal gas,the change in internal energy is given by $\Delta U = n \times C_v \times \Delta T$. Given $n = 5 \, mol$,$C_v = 28 \, J \, K^{-1} \, mol^{-1}$,and $\Delta T = 200 \, K - 100 \, K = 100 \, K$. $\Delta U = 5 \times 28 \times 100 = 14000 \, J = 14 \, kJ$. For an ideal gas,$\Delta (pV) = nR\Delta T$. Given $R = 8.0 \, J \, K^{-1} \, mol^{-1}$. $\Delta (pV) = 5 \times 8 \times 100 = 4000 \, J = 4 \, kJ$.

Class 11 Chemistry Thermodynamics Mix Examples-Thermodynamics and Thermochemistry

Difficult

$5 \, mol$ of an ideal gas at $100 \, K$ are allowed to undergo reversible compression till its temperature becomes $200 \, K$. If $C_v = 28 \, J \, K^{-1} \, mol^{-1}$,calculate $\Delta U$ and $\Delta pV$ for this process. $(R = 8.0 \, J \, K^{-1} \, mol^{-1})$

JEE MAIN 2019 All JEE MAIN

A
$\Delta U = 2.8 \, kJ ; \Delta (pV) = 0.8 \, kJ$
B
$\Delta U = 14 \, kJ ; \Delta (pV) = 4 \, kJ$
C
$\Delta U = 14 \, kJ ; \Delta (pV) = 18 \, kJ$
D
$\Delta U = 14 \, kJ ; \Delta (pV) = 0.8 \, J$

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Two statements are given below.
Statement $I$: The reaction $Cr_2O_3 + 2 Al \rightarrow Al_2O_3 + 2 Cr$ $(\Delta G^{\ominus} = -421 \ kJ)$ is thermodynamically feasible.
Statement $II$: The above reaction occurs at room temperature.
The correct answer is

MediumAP EAMCET 2024

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At $300 \, K$ temperature,the standard heat of formation of benzoic acid $(s)$,$CO_{2(g)}$,and $H_2O_{(l)}$ are $-408$,$-393$,and $-286 \, kJ \, mol^{-1}$ respectively. At constant pressure,the heat of combustion for benzoic acid will be $..... \, kJ$.

Medium

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For a reaction,$X_{2(g)} + Y_{2(g)} \rightleftharpoons 2XY_{(g)}$. If $\Delta G_r^o = 20 \ kJ \ mol^{-1}$ and $\Delta S_r^o = -20 \ J \ K^{-1} \ mol^{-1}$ at $200 \ K$. Calculate $\Delta H_r^o$ at $400 \ K$ (Given $\Delta_r C_P = 20 \ J \ K^{-1} \ mol^{-1}$).

Medium

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$A$ system consisting of $1 \, mole$ of an ideal gas undergoes a reversible process,$A$ $\rightarrow B$ $\rightarrow C$ $\rightarrow A$ (schematically indicated in the figure below). If the temperature at the starting point $A$ is $300 \, K$ and the work done in the process $B \rightarrow C$ is $1 \, L \, atm$,the heat exchanged in the entire process in $L \, atm$ is $....$

DifficultKVPY 2017

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For the reaction $2A_{(g)} + B_{(g)} \to 2D_{(g)}$,given $\Delta U^{\theta} = -10.5 \ kJ$ and $\Delta S^{\theta} = -44.1 \ J \ K^{-1}$. Calculate $\Delta G^{\theta}$ for the reaction at $298 \ K$ and predict whether the reaction may occur spontaneously.

Medium

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$5 \, mol$ of an ideal gas at $100 \, K$ are allowed to undergo reversible compression till its temperature becomes $200 \, K$. If $C_v = 28 \, J \, K^{-1} \, mol^{-1}$,calculate $\Delta U$ and $\Delta pV$ for this process. $(R = 8.0 \, J \, K^{-1} \, mol^{-1})$

Similar Questions

Two statements are given below.Statement $I$: The reaction $Cr_2O_3 + 2 Al \rightarrow Al_2O_3 + 2 Cr$ $(\Delta G^{\ominus} = -421 \ kJ)$ is thermodynamically feasible.Statement $II$: The above reaction occurs at room temperature.The correct answer is

At $300 \, K$ temperature,the standard heat of formation of benzoic acid $(s)$,$CO_{2(g)}$,and $H_2O_{(l)}$ are $-408$,$-393$,and $-286 \, kJ \, mol^{-1}$ respectively. At constant pressure,the heat of combustion for benzoic acid will be $..... \, kJ$.

For a reaction,$X_{2(g)} + Y_{2(g)} \rightleftharpoons 2XY_{(g)}$. If $\Delta G_r^o = 20 \ kJ \ mol^{-1}$ and $\Delta S_r^o = -20 \ J \ K^{-1} \ mol^{-1}$ at $200 \ K$. Calculate $\Delta H_r^o$ at $400 \ K$ (Given $\Delta_r C_P = 20 \ J \ K^{-1} \ mol^{-1}$).

For the reaction $2A_{(g)} + B_{(g)} \to 2D_{(g)}$,given $\Delta U^{\theta} = -10.5 \ kJ$ and $\Delta S^{\theta} = -44.1 \ J \ K^{-1}$. Calculate $\Delta G^{\theta}$ for the reaction at $298 \ K$ and predict whether the reaction may occur spontaneously.

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Two statements are given below.
Statement $I$: The reaction $Cr_2O_3 + 2 Al \rightarrow Al_2O_3 + 2 Cr$ $(\Delta G^{\ominus} = -421 \ kJ)$ is thermodynamically feasible.
Statement $II$: The above reaction occurs at room temperature.
The correct answer is