Question 1: 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]
![](https://app-content.cdn.examgoal.net/fly/@width/image/1l71iiut6/83602338-b0f9-42b1-947b-b3b779d74f3e/5af2d690-2050-11ed-8203-e546d9e69fa3/file-1l71iiut7.png?format=png)

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.
![](https://imagex.cdn.examgoal.net/1ksn7f5bw/ca82b57c-f934-48c6-8b8f-7fa61b67030f/ef059fc0-0346-11ec-aa1c-d9fff7d3eb63/file-1ksn7f5bx.jpeg)

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: