Chemistry, asked by OxOAnuRadhaOxO, 10 months ago

One mole of am ideal Monatomic gas at temperature T and Volume 1L expands to 2L against a constant external pressure of one atm under adiabatic conditions, then final temperature of gas will be?

Answers

Answered by sahildhande987

$\huge{\underline{\underline{\tt{\red{Answer}}}}}$

Given:

________________________________________

★ Number of moles of monoatomic gas: 1

★ External Pressure = Irreversible Process

★ Volume Expands from 1L to 2L

★ Pressure = 1atm

★ Adiabatic condition

________________________________________

$\huge{\underline{\underline{\green{\tt{Formula}}}}}$

✪ $nC_v \triangle T = -P_{ext} \triangle V$ ✪

__________________________________

$\huge{\underline{\tt{SoluTion}}}$

For monoatomic gas $C_v = \dfrac{3R}{2}$

Applying this in the formula given above

$\implies 1\times \dfrac{3R}{2} \times (T_2 -T_1) = -1 \times(2-1) \\ \\ \implies (T_2-T_1) = \dfrac{-2}{3 \times R} \\ \\ \implies (T_2-T_1)= \dfrac{-2}{3 \times 0.0821} \\ \\ \implies{\boxed{T_2= T_1- \dfrac{2}{3\times 0.0821}}} (by putting R= 0.0821) \\ \\ \: \: \: \: \: \boxed{OR} \\ \\ \implies \boxed{T_2= T_1- 6} \bigg(by putting R=\dfrac{1}{12}\bigg)$