Question 1: Thermodynamics & KTG

Question

In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by T$\Delta $X where T is temperature of the system and $\Delta $X is the infinitesimal change in a thermodynamic quantity X of the system. For a mole of monatomic ideal gas, $X = {3 \over 2}R\,\ln \left( {{T \over {{T_A}}}} \right) + R\,\ln \left( {{V \over {{V_A}}}} \right)$
Here, R is gas constant, V is volume of gas, T
A
and V
A
are constants.
The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities.
![](https://imagex.cdn.examgoal.net/1kt3lpc5y/b4203eb8-01d4-4e15-9690-b4b8a8b38545/5497ae70-0c4b-11ec-a7b0-c3f7d2fd429a/file-1kt3lpc5z.jpeg)

Accepted Answer

1-2 process is isothermal and 2-3 process is isochoric.
(I) ${W_{1 	o 2}} = nRI\,\ln {{{V_f}} \over {{V_i}}} = 1 	imes R{{{T_0}} \over 3}\,\ln {{{V_2}} \over {{V_1}}}$
W
2$ 	o $3
= 0 (Isochoric process)
${W_{1 	o 2 	o 3}}$ = ${W_{1 	o 2}}$ + ${W_{2 	o 3}}$
= ${{R{T_0}} \over 3}$ ln 2(I$ 	o $P)
(II) $\Delta U = {f \over 2}nR({T_f} - {T_i})$
$\Delta {U_{1 	o 2 	o 3}} = {3 \over 2}\left[ {{T_0} - {{{T_0}} \over 3}} ight]$
$ = R{T_0}$ (II$ 	o $R)
(III) ${Q_{1 	o 2 	o 3}} = \Delta {U_{1 	o 2 	o 3}} + {W_{1 	o 2 	o 3}}$
(First law of thermodynamics)
$ = R{T_0} + {{R{T_0}} \over 3}\ln 2$
${{R{T_0}} \over 3}[3 + \ln 2]$ (III$ 	o $T)
(IV) ${Q_{1 	o 2}} = \Delta {U_{1 	o 2}} + {W_{1 	o 2}} = 0 + {{R{T_0}} \over 3}ln2 = {{R{T_0}} \over 3}ln2$ (IV$ 	o $P)

Answer

I $ 	o $ P, II $ 	o $ R, III $ 	o $ T, IV $ 	o $ S

Answer

I $ 	o $ P, II $ 	o $ T, III $ 	o $ Q, IV $ 	o $ T

Answer

I $ 	o $ S, II $ 	o $ T, III $ 	o $ Q, IV $ 	o $ U

Answer

I $ 	o $ P, II $ 	o $ R, III $ 	o $ T, IV $ 	o $ P

Thermodynamics & KTG

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