Question 134: 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, TA and VA are constants.The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities.

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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