Question 91: Thermodynamics & KTG

Question

One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature (V-T) diagram. The correct statement(s) is/are [R is the gas constant]

Accepted Answer

P-V graph of the given V-T graph is shown below.
(d) $$\left| {{{\Delta {Q_{1 	o 2}}} \over {\Delta {Q_{3 	o 4}}}}} ight| = \left| {{{N{C_p}\Delta {T_{1 	o 2}}} \over {N{C_p}\Delta {T_{3 	o 4}}}}} ight| = {{{T_0}} \over {{T_0}/2}} = 2$$
(b) $$\left| {{{\Delta {Q_{1 	o 2}}} \over {\Delta {Q_{2 	o 3}}}}} ight| = \left| {{{N{C_p}\Delta {T_{1 	o 2}}} \over {N{C_p}\Delta {T_{3 	o 4}}}}} ight| = {{{C_p}} \over {{C_V}}} = {5 \over 3}$$
(a) $${W_{cycle}} = {p_0}{V_0} = nR\left[ {{{{T_0}} \over 2}} ight]$$
Note For ideal gas equation,
pV = nRT
$$ 	herefore $$ (pV)
4
= (nRT)
4
or p
0
V
0
= $$nR{{{T_0}} \over 2}$$ = $$R{{{T_0}} \over 2}$$
as n = 1
(c) Wrong as no adiabatic process is involved.

Answer

Work done in this thermodynamic cycle (1$$ 	o $$2$$ 	o $$3$$ 	o $$4$$ 	o $$1) is $$\left| W ight| = {1 \over 2}R{T_0}$$.

Answer

The ratio of heat transfer during processes 1$$ 	o $$2 and 2$$ 	o $$3 is $$\left| {{{{Q_{1 	o 2}}} \over {{Q_{2 	o 3}}}}} ight| = {5 \over 3}$$

Answer

The above thermodynamic cycle exhibits only isochoric and adiabatic processes.

Answer

The ratio of heat transfer during processes 1$$ 	o $$2 and 3$$ 	o $$4 is $$\left| {{{{Q_{1 	o 2}}} \over {{Q_{3 	o 4}}}}} ight| = {1 \over 2}$$

Thermodynamics & KTG

One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature (V-T) diagram. The correct statement(s) is/are [R is the gas constant]

Choose the correct answer: