In a thermodynamic process two moles of a monatomic ideal gas obeys P - V-2- If temperature of the gas increases from 300 K to 400 K- then find work done by the gas where R-universal gas constant

The correct option is A 200 RGiven, P∝ V^ 2 n=2 T_1=300K T_2=400K PV^2=const . . . . . .(1) γ=2 #160; #160; #160; #160 ...

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Byju's Answer

Standard XII

Chemistry

Liquefaction of Gases and Critical Constants

In a thermody...

Question

In a thermodynamic process two moles of a monatomic ideal gas obeys P $\propto V^{- 2}$ . If temperature of the gas increases from 300 K to 400 K, then find work done by the gas (where $R =$ universal gas constant)

200 R

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-200 R

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-100 R

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-400 R

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Solution

The correct option is A -200 R
Given,
$P \propto V^{- 2}$
$n = 2$
$T_{1} = 300 K$
$T_{2} = 400 K$
$P V^{2} = c o n s t$ . . . . . .(1)
$γ = 2$ ( $P V^{γ} = c o n s t a n t$ )
The above equation shows that the process is adiabatic process,
The work done in adiabatic process in thermodynamics is given by
$W = n R \frac{(T_{1} - T_{2})}{γ - t}$
$W = n R \frac{(300 - 400)}{2 - 1}$
$W = - 100 n R = - 2 \times 100 R$
$W = - 200 R$
The correct option is B.

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In a thermodynamic process two moles of a monatomic ideal gas obeys P ∝V−2. If temperature of the gas increases from 300 K to 400 K, then find work done by the gas (where R=universal gas constant)

In a thermodynamic process two moles of a monatomic ideal gas obeys P $\propto V^{- 2}$ . If temperature of the gas increases from 300 K to 400 K, then find work done by the gas (where $R =$ universal gas constant)