D. C. Pandey Solutions for Chapter: Laws of Thermodynamics, Exercise 5: Exercises

The temperature of a monatomic gas is increased from $T_0$ to $2T_0$ in three different processes such as isochoric, isobaric and adiabatic. Heat given to the gas in these three processes are $Q_1$, $Q_2$ and $Q_3$, respectively. Then, choose the correct option.

A cyclic process $1-2-3-4-1$ is depicted on $V-T$ diagram. The $p-T$ and $p-V$ diagrams for this cyclic process are given below. Select the correct choices (more than one options is/are correct)

One mole of a monatomic ideal gas is taken along the cycle $\mathrm{ABCA}$ as shown in the diagram.

The ratio of specific heat in the process $CA$ to the specific heat in the process $BC$ is

One mole of a monoatomic ideal gas is taken through the cycle $ABCDA$ as shown in the figure.

$T_A=1000 \mathrm{K} \text{and} \mathit{2}{p}_A\mathit{=}\mathit{3}{p}_B\mathit{=}\mathit{6}{p}_C$

The temperature at $B$ is

$\left[\text{Assume }{\left(\frac{2}{3}\right)}^{0.4}=0.85 \text{and }R=\frac{25}{3}\mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}\right]$

One mole of a monoatomic ideal gas is taken through the cycle $ABCDA$ as shown in the figure.

$T_A=1000 \mathrm{K} \text{and} \mathit{2}{p}_A\mathit{=}\mathit{3}{p}_B\mathit{=}\mathit{6}{p}_C$

Work done by gas in the process $A\to B$ is

$\left[\text{Assume }{\left(\frac{2}{3}\right)}^{0.4}=0.85 \text{and }R=\frac{25}{3}\mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}\right]$

One mole of a monoatomic ideal gas is taken through the cycle $ABCDA$ as shown in the figure.

$T_A=1000 \mathrm{K} \text{and} \mathit{2}{p}_A\mathit{=}\mathit{3}{p}_B\mathit{=}\mathit{6}{p}_C$

Heat lost by the gas in the process $B\to C$ is

$\left[\text{Assume }{\left(\frac{2}{3}\right)}^{0.4}=0.85 \text{and }R=\frac{25}{3}\mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}\right]$

The pressure versus temperature $(p\mathit{-}T)$ graph of $n \mathrm{moles}$ of an ideal gas is shown in the figure. Plot the corresponding,
$\left(\mathrm{a}\right)$ density versus volume $(\rho -V)$ graph
$\left(\mathrm{b}\right)$ pressure versus volume $(p-V)$ graph and
$\left(\mathrm{c}\right)$ density versus pressure $(\rho -p)$ graph.

Three moles of an ideal gas being initially at a temperature $T_{\mathrm{i}}=273 \mathrm{K}$ were isothermally expanded $5$ times its initial volume and then isochorically heated so that the pressure in the final state becomes equal to that in the initial state. The total heat supplied in the process is $80 \mathrm{kJ}$. Find $\gamma \left(=\frac{C_{\mathrm{p}}}{C_{\mathrm{V}}}\right)$ of the gas.