Thermodynamics – Page 2

Particle in a tube

January 16th, 2022jeefirst0 Comments

JEE Advanced 2019 Paper 2, Question 3

A small particle of mass $m$ moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from the closed end is $L=L_{0}$ the particle speed is $v=v_{0} .$ The piston is moved inward at a very low speed $V$ such that $V \ll \frac{{\rm d} L}{L} v_{0}$ , where ${\rm d} L$ is the infinitesimal displacement of the piston. Which of …

Thermodynamic cycle on a VT diagram

January 1st, 2022jeefirst0 Comments

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

Rod heated by wire

December 30th, 2021jeefirst0 Comments

JEE Advanced 2019 Paper 1, Question 3

A current carrying wire heats a metal rod. The wire provides a constant power $P$ to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature $T$ in the metal rod changes with time $t$ as