An ideal gas in a thermally insulated vessel at internal pressure =...

An ideal gas in a thermally insulated vessel at internal pressure = ${P}_{1}$ , volume = ${V}_{1}$ and absolute temperature = ${T}_{1}$ expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are ${P}_{2}$ , ${V}_{2}$ and ${T}_{2}$ , respectively. For this expansion,

An ideal gas in a thermally insulated vessel at internal pressure = P _ 1 , volume = V _ 1 and absolute temperature = T

Options

A $q = 0$
B ${T}_{2} = {T}_{1}$
C ${P}_{2}{V}_{2} = {P}_{1}{V}_{1}$
D ${P}_{2}{V}_{2}^{\gamma} = {P}_{1}{V}_{1}^{\gamma}$

Correct answer

A. $q = 0$

Step-by-step solution

Since container is thermally insulated. So, q = 0, and it is a case of free expansion therefore W = 0 and

∆ E = 0

So,

{T}_{1} = {T}_{2}

Also,

{P}_{1}{V}_{1} = {P}_{2}{V}_{2}

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