Match the following from Table A- in the case of gases- with those in Table B-Table - ATable - Ba Work done in isobaric processd nRTlog e V 2 - V 1 b Wok done in isothermal processe P V 2 - V 1 c Work done in adiabatic processf nRT T 1 - T 2 - -1g Zero

The correct option is B a→ e,b→ d,c→ f Work done in isobaric process= ∫_V_1^V_2 PdV =P∫^V_2_V_1dV =P(V_2 V_1) Work done in isothermal proces ...

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Standard XII

Physics

Work

Match the fol...

Question

Match the following from Table A, in the case of gases, with those in Table B.
Table - A Table - B
(a) Work done in isobaric process (d) $n R T {log}_{e} (\frac{V_{2}}{V_{1}})$
(b) Wok done in isothermal process (e) $P (V_{2} - V_{1})$
(c) Work done in adiabatic process (f) $\frac{n R T (T_{1} - T_{2})}{γ - 1}$
(g) Zero

a \to h, b \to g, c \to e

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a \to e, b \to d, c \to g

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a \to g, b \to h, c \to e

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a \to e, b \to d, c \to f

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Solution

The correct option is B $a \to e, b \to d, c \to f$
Work done in isobaric process= $\int_{V_{1}}^{V_{2}} P d V$
$= P \int_{V_{1}}^{V_{2}} d V$
$= P (V_{2} - V_{1})$
Work done in isothermal process= $\int_{V_{1}}^{V_{2}} P d V$
$= \int_{V_{1}}^{V_{2}} \frac{n R T}{V} d V$
$= n R T l n (\frac{V_{2}}{V_{1}})$
Work done in adiabatic process= $\int_{V_{1}}^{V_{2}} P d V$
$= \int_{V_{1}}^{V_{2}} k V^{- γ} d V$
where $k = P V^{γ}$
$= n R T \times \frac{T_{1} - T_{2}}{γ - 1}$
Hence correct answer is option D.

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Table - A	Table - B
(a) Work done in isobaric process	(d) $n R T {log}_{e} (\frac{V_{2}}{V_{1}})$
(b) Wok done in isothermal process	(e) $P (V_{2} - V_{1})$
(c) Work done in adiabatic process	(f) $\frac{n R T (T_{1} - T_{2})}{γ - 1}$
	(g) Zero

Match the following from Table A, in the case of gases, with those in Table B.Table - ATable - B(a) Work done in isobaric process(d) nRTloge(V2V1)(b) Wok done in isothermal process(e) P(V2−V1)(c) Work done in adiabatic process(f) nRT(T1−T2)γ−1(g) Zero

The correct option is B a→e,b→d,c→fWork done in isobaric process=∫V2V1PdV=P∫V2V1dV=P(V2−V1)Work done in isothermal process=∫V2V1PdV=∫V2V1nRTVdV=nRTln(V2V1)Work done in adiabatic process=∫V2V1PdV=∫V2V1kV−γdVwhere k=PVγ=nRT×T1−T2γ−1Hence correct answer is option D.