Embibe Experts Solutions for Chapter: Thermodynamics, Exercise 1: Level 1

A system is taken from state $i$ to state $f$via two different paths.

$i )$ Path $iaf$ with $Q=50 \mathrm{cal}$ and $W=20 \mathrm{cal}.$

$ii )$  Path $ibf, Q=36 \mathrm{cal}.$ 

Find the value of $W$ (in $\mathrm{cal}$) for the second path.

Consider $R$ to be the universal gas constant. Given that, the amount of heat needed to raise the temperature of $2\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{s}$ of an ideal monatomic gas from $273\mathrm{ }\mathrm{K}$ to $373\mathrm{ }\mathrm{K}$ when no work is done is $n\times R$. Then $n$ is

A given quantity of gas is taken from the state $\mathrm{A}$ to the state $\mathrm{C}$ reversibly by two paths, $\mathrm{A}\to \mathrm{C}$ directly and $\mathrm{A} \to \mathrm{B}\to \mathrm{C}$ as shown in the figure below:

During the process $\mathrm{A}\to \mathrm{C}$, work done by the gas is $100 \mathrm{J}$ and heat absorbed is $120 \mathrm{J}$. If during the process $\mathrm{A}\to \mathrm{B}\to \mathrm{C}$, the work done by the gas is $80 \mathrm{J}$, the heat absorbed is

$32 \mathrm{g}$ of ${\mathrm{O}}_2$ is contained in a cubical container of side $1 \mathrm{m}$ and maintained at a temperature of $127 °\mathrm{C}$. The isothermal bulk modulus of elasticity of the gas in terms of universal gas constant $R$ is $aR$. Find the value of $a$.

A gas with the ratio of specific heat $y$ expands from an initial pressure of $p_1$ and volume $V_1$ to pressure $p_2$ and volume $V_2\text{,}$ adiabatically. The work done is given by

The net amount of the work done in the following indicator diagram is -

A heat engine operating between $40$ degrees $C$ and $380$ degrees $C$ has an efficiency $60\%$ of that of a Carnot engine operating between the same temperatures. If the engine absorbs heat at a rate of $60 kW$, at what rate does it exhaust heat (in $kW$ )? (Approximate the answer to the nearest integer.)

An ideal heat engine exhausting heat at $77°\mathrm{C}$ is to have a $30\%$ efficiency. Find the temperature$\left(\text{in} °\mathrm{C}\right)$ at which it must take heat.