When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas, is
IIT 1990, Medium
Download our app for free and get started
(d) Fraction of supplied energy which in creases the internal energy is given by
$f = \frac{{\Delta U}}{{{{(\Delta Q)}_P}}} = \frac{{{{(\Delta Q)}_V}}}{{{{(\Delta Q)}_P}}} = \frac{{\mu {C_V}\Delta T}}{{\mu {C_P}\Delta T}} = \frac{1}{\gamma }$
For diatomic gas $\gamma = \frac{7}{5}$==> $f = \frac{5}{7}$
$f = \frac{{\Delta U}}{{{{(\Delta Q)}_P}}} = \frac{{{{(\Delta Q)}_V}}}{{{{(\Delta Q)}_P}}} = \frac{{\mu {C_V}\Delta T}}{{\mu {C_P}\Delta T}} = \frac{1}{\gamma }$
For diatomic gas $\gamma = \frac{7}{5}$==> $f = \frac{5}{7}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A Carnot engine operates between ${227^o}C$ and ${27^o}C.$ Efficiency of the engine will beView Solution
- 2$1\,kg$ of water at $100\, ^{\circ}C$ is converted into steam at $100^{\circ}\,C$ by boiling at atmospheric pressure. The volume of water changes from $1.00 \times 10^{-3}\,m ^3$ as a liquid to $1.671\,m ^3$ as steam. The change in internal energy of the system during the process will be $........kJ$ (Given latent heat of vaporisaiton $=2257\,kJ / kg$. Atmospheric pressure $=1 \times 10^5\,Pa$ )View Solution
- 3A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from $V$ to $32\ V$, the efficiency of the engine isView Solution
- 4In a Carnot engine, when ${T_2} = {0^o}C$ and ${T_1} = {200^o}C,$ its efficiency is ${\eta _1}$ and when ${T_1} = 0{\,^o}C$ and ${T_2} = - 200{\,^o}C$, Its efficiency is ${\eta _2}$, then what is ${\eta _1}/{\eta _2}$View Solution
- 5In the $p-V$ diagram below, the dashed curved line is an adiabat.For a process that is described by a straight line joining two points $X$ and $Y$ on the adiabat (solid line in the diagram) heat is (Hint consider the variation in temperature from $X$ to $Y$ along the straight line)View Solution
- 6In a certain thermodynamical process, the pressure of a gas depends on its volume as $kV ^{3}$. The work done when the temperature changes from $100^{\circ} C$ to $300^{\circ} C$ will be .......... $nR$, where $n$ denotes number of moles of a gas.View Solution
- 7$Assertion :$ The heat supplied to a system is always equal to the increase in its internal energy.View Solution
$Reason :$ When a system changes from one thermal equilibrium to another, some heat is absorbed by it. - 8A thermodynamic system is taken from an original state $A$ to an intermediate state $B$ by a linear process as shown in the figure. It's volume is then reduced to the original value from $B$ to $C$ by an isobaric process. The total work done by the gas from $A$ to $B$ and $B$ to $C$ would be :View Solution
- 9Two carnot engines $A$ and $B$ operate in series such that engine $A$ absorbs heat at $T_{1}$ and rejects heat to a sink at temperature $T$. Engine $B$ absorbs half of the heat rejected by engine $A$ and rejects heat to the sink at ${T}_{3}$. When workdone in both the cases is equal, the value of ${T}$ isView Solution
- 10An insulator container contains $4\, moles$ of an ideal diatomic gas at temperature $T.$ Heat $Q$ is supplied to this gas, due to which $2 \,moles$ of the gas are dissociated into atoms but temperature of the gas remains constant. ThenView Solution