(B) For an isothermal expansion of an ideal gas in a vacuum (free expansion),the external pressure $P_{ext} = 0$.Since work done $W = -P_{ext} \Delta

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(B) For an isothermal expansion of an ideal gas in a vacuum (free expansion),the external pressure $P_{ext} = 0$.Since work done $W = -P_{ext} \Delta V$,the work done is $0$.According to the first law of thermodynamics,$\Delta U = q + W$.For an isothermal process of an ideal gas,the internal energy $\Delta U$ depends only on temperature.Since the temperature is constant $(\Delta T = 0)$,the change in internal energy $\Delta U = 0$.

Class 11 Chemistry Thermodynamics First law of thermodynamics

Medium

For $1 \, \text{mol}$ of an ideal gas,isothermal expansion occurs from $1 \, \text{L}$ to $10 \, \text{L}$ in a vacuum at $300 \, \text{K}$. What is the value of $\Delta U$ for this process? $(R = 2 \, \text{cal} \, \text{K}^{-1} \, \text{mol}^{-1})$

A
$163.7 \, \text{cal}$
B
$0$
C
$1381.1 \, \text{cal}$
D
$9 \, \text{L} \cdot \text{atm}$

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Thermodynamics

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First law of thermodynamics

$A$ gas is allowed to expand in an insulated container against a constant external pressure of $2.5 \ atm$ from $2.5 \ L$ to $4.5 \ L$. The change in internal energy of the gas in joules is: (in $J$)

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An engine absorbs heat $Q_1$ at temperature $T_1$ and heat $Q_2$ at temperature $T_2$. The work done by the engine is given as $W = Q_1 + Q_2$. Which of the following statements is correct?

Easy

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$2.5 \ kJ$ of work is done on the system and it releases $1500 \ J$ of heat. What is the change in internal energy (in $J$)?

MediumMHT CET 2020

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For combustion of one mole of magnesium in an open container at $300 \ K$ and $1 \ bar$ pressure,$\Delta_{C}H^{\ominus} = -601.70 \ kJ \ mol^{-1}$,the magnitude of change in internal energy for the reaction is $.... \ kJ$. (Nearest integer)
(Given : $R = 8.3 \ J \ K^{-1} \ mol^{-1}$ )

MediumJEE MAIN 2022

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For the reaction $PCl_{5(g)} \to PCl_{3(g)} + Cl_{2(g)}$,which of the following relations is correct?

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For $1 \, \text{mol}$ of an ideal gas,isothermal expansion occurs from $1 \, \text{L}$ to $10 \, \text{L}$ in a vacuum at $300 \, \text{K}$. What is the value of $\Delta U$ for this process? $(R = 2 \, \text{cal} \, \text{K}^{-1} \, \text{mol}^{-1})$

Similar Questions

$A$ gas is allowed to expand in an insulated container against a constant external pressure of $2.5 \ atm$ from $2.5 \ L$ to $4.5 \ L$. The change in internal energy of the gas in joules is: (in $J$)

An engine absorbs heat $Q_1$ at temperature $T_1$ and heat $Q_2$ at temperature $T_2$. The work done by the engine is given as $W = Q_1 + Q_2$. Which of the following statements is correct?

$2.5 \ kJ$ of work is done on the system and it releases $1500 \ J$ of heat. What is the change in internal energy (in $J$)?

For combustion of one mole of magnesium in an open container at $300 \ K$ and $1 \ bar$ pressure,$\Delta_{C}H^{\ominus} = -601.70 \ kJ \ mol^{-1}$,the magnitude of change in internal energy for the reaction is $.... \ kJ$. (Nearest integer)(Given : $R = 8.3 \ J \ K^{-1} \ mol^{-1}$ )

For the reaction $PCl_{5(g)} \to PCl_{3(g)} + Cl_{2(g)}$,which of the following relations is correct?

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For combustion of one mole of magnesium in an open container at $300 \ K$ and $1 \ bar$ pressure,$\Delta_{C}H^{\ominus} = -601.70 \ kJ \ mol^{-1}$,the magnitude of change in internal energy for the reaction is $.... \ kJ$. (Nearest integer)
(Given : $R = 8.3 \ J \ K^{-1} \ mol^{-1}$ )