Embibe Experts Solutions for Chapter: Thermodynamics, Exercise 2: Level 2

A work of $146 \mathrm{kJ}$ is performed on the gas, in order to compress one-kilo mole of gas adiabatically and into this process the temperature of the gas increases by $7°\mathrm{C}.$ The gas is $\left(R=8.3 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}\right)$

An ideal gas undergoes a quasi-static, reversible process in which its molar heat capacity $C$ remains constant. If during this process, the relation of pressure $P$ and volume $V$ is given by, $P{V}^{\mathrm{n}}=$constant, then $n$ is given by ($C_{\mathrm{P}}=$molar specific heat at constant pressure, $C_{\mathrm{V}}=$molar specific heat at constant volume),

At low temperatures, the molar heat capacity of solids at constant pressure depends on the absolute temperature $T$ according to the law $C_T=C_{T_0}{\left(\frac{T}{T_0}\right)}^3.$ One mole $(40 \mathrm{g})$ of solid argon at temperature $8 \mathrm{K}$ is brought into thermal contact with $2 \mathrm{kg}$ of solid argon at a temperature of $1 \mathrm{K}$ and they insulated everything together. What will be the temperature (in $\mathrm{K}$ ) of the substance when thermal equilibrium is established? Round off to nearest integer.

A closed vessel contains $0.1$ mole of a monoatomic ideal gas at $200 \mathrm{K}.$ If $0.05$ mole of the same gas at $400 \mathrm{K}$ is added to it, the final equilibrium temperature (in $\mathrm{K}$) of the gas in the vessel will be close to _______.

(Note: Round off the answer to nearest integer)

One gram-mole of an ideal gas $A$ with the ratio of constant pressure and constant volume specific heats, ${\gamma }_{\mathrm{A}}=\frac{5}{3}$ is mixed with $n$ gram-moles of another ideal gas $B$ with ${\gamma }_{\mathrm{B}}=\frac{7}{5}$. If the $\gamma$ for the mixture is $\frac{19}{13}$ what will be the value of $n\text{?}$

A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

A Carnot reversible engine converts $1/6$ of heat input into work. When the temperature of the sink is reduced by $62 \mathrm{K}$, the efficiency of Carnot's cycle becomes $1/3$. What is the sum of the temperature (in kelvin) of the source and the sink?

A Carnot engine whose sink is at $300 \mathrm{K}$ has an efficiency of $40\%$. By how much should the temperature of source be increased so as to increase its efficiency by $50\%$ of original efficiency?