# NEET Physics Thermodynamics Questions Solved

Work done by a system under isothermal change from a volume V1 to V2 for a gas which obeys Vander Waal's equation $\left(V-\beta n\right)\text{\hspace{0.17em}}\left(P+\frac{\alpha {n}^{2}}{V}\right)=nRT$

(1) $nRT{\mathrm{log}}_{e}\left(\frac{{V}_{2}-n\beta }{{V}_{1}-n\beta }\right)+\alpha \text{\hspace{0.17em}}{n}^{2}\text{\hspace{0.17em}}\left(\frac{{V}_{1}-{V}_{2}}{{V}_{1}{V}_{2}}\right)$

(2) $nRT{\mathrm{log}}_{10}\left(\frac{{V}_{2}-\alpha \beta }{{V}_{1}-\alpha \beta }\right)+\alpha \text{\hspace{0.17em}}{n}^{2}\text{\hspace{0.17em}}\left(\frac{{V}_{1}-{V}_{2}}{{V}_{1}{V}_{2}}\right)$

(3) $nRT{\mathrm{log}}_{e}\left(\frac{{V}_{2}-n\alpha }{{V}_{1}-n\alpha }\right)+\beta \text{\hspace{0.17em}}{n}^{2}\text{\hspace{0.17em}}\left(\frac{{V}_{1}-{V}_{2}}{{V}_{1}{V}_{2}}\right)$

(4) $nRT{\mathrm{log}}_{e}\left(\frac{{V}_{1}-n\beta }{{V}_{2}-n\beta }\right)+\alpha \text{\hspace{0.17em}}{n}^{2}\text{\hspace{0.17em}}\left(\frac{{V}_{1}{V}_{2}}{{V}_{1}-{V}_{2}}\right)$

(1) According to given Vander Waal’s equation

$P=\frac{nRT}{V-n\beta }-\frac{\alpha {n}^{2}}{{V}^{2}}$

Work done, $W={\int }_{{V}_{1}}^{{V}_{2}}PdV=nRT{\int }_{{V}_{1}}^{{V}_{2}}\frac{dV}{V-n\beta }-\alpha {n}^{2}{\int }_{{V}_{1}}^{{V}_{2}}\frac{dV}{{V}^{2}}$

$=nRT\text{\hspace{0.17em}}\left[{\mathrm{log}}_{e}\left(V-n\beta \right)\right]{\text{\hspace{0.17em}}}_{{V}_{1}}^{{V}_{2}}+\alpha {n}^{2}{\left[\frac{1}{V}\right]}_{{V}_{1}}^{{V}_{2}}$

$=nRT{\mathrm{log}}_{e}\frac{{V}_{2}-n\beta }{{V}_{1}-n\beta }+\alpha {n}^{2}\left(\frac{{V}_{1}-{V}_{2}}{{V}_{1}{V}_{2}}\right)$

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