N moles of a van der Waals' gas obeying equation of state left(p+frac{n^2 a}{V^2}right)(V-n b)=n

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11.Thermodynamics

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$n$ moles of a van der Waals' gas obeying the equation of state $\left(p+\frac{n^2 a}{V^2}\right)(V-n b)=n R T$, where $a$ and $b$ are gas dependent constants, is made to undergo a cyclic process that is depicted by a rectangle in the $p-V$ diagram as shown below. What is the heat absorbed by the gas in one cycle?

A

$n\left(p_1-p_2\right)\left(V_2-V_1\right)$

B

$\left(p_1-p_2\right)\left(V_2-V_1\right)$

C

$\left(p_1+\frac{n^2 a}{V_1^2}-p_2-\frac{n^2 a}{V_2^2}\right)\left(V_1-V_2\right)$

D

$\left(p_1+\frac{n^2 a}{V_1^2}-p_2-\frac{n^2 a }{V_2^2}\right)\left(V_2-V_1\right)$

(KVPY-2009)

Solution

(b)

Work done $=$ Arca enclosed under $p \cdot V$ diagram $=\left(p_1-p_2\right)\left(V_2-V_1\right)$

Standard 11

Physics

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