1, mole of an ideal monoatomic gas at temperature 'T_0' expands slowly according to law P =

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11.Thermodynamics

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$1\, mole$ of an ideal monoatomic gas at temperature $'T_0'$ expands slowly according to the law $P = KV$, where $K$ is a constant. If the final temperature of the gas is $2T_0$. Find the heat supplied to the gas

$\frac{{2{T_0}}}{2}$

${2{T_0}}$

${2RT}$

$\frac{3}{2}\,R{T_0}$

Solution

$\mathrm{Q}=\Delta \mathrm{U}+\Delta \mathrm{w}$

$\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}=1 \times \frac{3}{2} \mathrm{R} \times\left(2 \mathrm{T}_{0}-\mathrm{T}_{0}\right)=\frac{3}{2} \mathrm{RT}_{0}$

Work $=\frac{\mu R \Delta T}{n-1}=\frac{1 \times R \times\left(2 T_{0}-T_{0}\right)}{2} \Rightarrow\left(\frac{R T_{0}}{2}\right)$

$\mathrm{Q}=\frac{3}{2} \mathrm{RT}_{0}+\frac{\mathrm{RT}_{0}}{2}$

$=2 \mathrm{RT}_{0}$

Standard 11

Physics

A closed vessel contains $0.1$ mole of a monoatomic ideal gas at $200\, K$. If $0.05$ mole of the same gas at $400\, K$ is added to it, the final equilibrium temperature (in $K$ ) of the gas in the vessel will be closed to

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(JEE MAIN-2020)

An ideal gas is taken from state $1$ to state $2$ through optional path $A, B, C \& D$ as shown in $P-V$ diagram. Let $Q, W$ and $U$ represent the heat supplied, work done $\&$ internal energy of the gas respectively. Then

normal

A system goes from $A$ to $B$ via two processes $I$ and $II$ as shown in figure. If $\Delta {U_1}$ and $\Delta {U_2}$ are the changes in internal energies in the processes $I$ and $II$ respectively, then

easy

(AIPMT-2013)

The $P-V$ diagram of a system undergoing thermodynamic transformation is shown in figure. The work done on the system in going from $A → B → C$ is $50 J$ and $ 20\, cal$ heat is given to the system. The change in internal energy between $A$ and $C$ is …… $J$

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Pressure versus temperature graph of an ideal gas is shown in figure

medium

$1\, mole$ of an ideal monoatomic gas at temperature $'T_0'$ expands slowly according to the law $P = KV$, where $K$ is a constant. If the final temperature of the gas is $2T_0$. Find the heat supplied to the gas

Solution

Similar Questions

A closed vessel contains $0.1$ mole of a monoatomic ideal gas at $200\, K$. If $0.05$ mole of the same gas at $400\, K$ is added to it, the final equilibrium temperature (in $K$ ) of the gas in the vessel will be closed to

An ideal gas is taken from state $1$ to state $2$ through optional path $A, B, C \& D$ as shown in $P-V$ diagram. Let $Q, W$ and $U$ represent the heat supplied, work done $\&$ internal energy of the gas respectively. Then

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The $P-V$ diagram of a system undergoing thermodynamic transformation is shown in figure. The work done on the system in going from $A → B → C$ is $50 J$ and $ 20\, cal$ heat is given to the system. The change in internal energy between $A$ and $C$ is …… $J$

Pressure versus temperature graph of an ideal gas is shown in figure

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