Thermodynamic cycle on a VT diagram

JEE Advanced 2019 Paper 1, Question 9

One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume vs. temperature (VT) diagram. The correct statement(s) is/are:

[R is the gas constant]

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  1. Work done in this thermodynamic cycle (1 \to 2 \to 3 \to 4 \to 1) is |W| = \frac{1}{2} R T_0.
  2. The above thermodynamic cycle exhibits only isochoric and adiabatic processes.
  3. The ratio of heat transfer during processes 1 \to 2 and 2 \to 3 is \left| \frac{Q_{1 \to 2}}{Q_{2 \to 3}} \right| = \frac{5}{3}.
  4. The ratio of heat transfer during processes 1 \to 2 and 3 \to 4 is \left| \frac{Q_{1 \to 2}}{Q_{3 \to 4}} \right| = \frac{1}{2}.

Related article: Thermodynamic processes on an ideal gas

Solution

An ideal gas obeys the relations

(1)   \begin{equation*}   \text{The ideal gas law: } P V = n R T \end{equation*}

(2)   \begin{equation*}   \text{Work done {\it by} the gas: } W = \int_a^b P dV \end{equation*}

(3)   \begin{equation*}   \text{Internal energy of a monatomic gas: } U = \frac{3}{2} n R T \end{equation*}

We …

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