1 ,,kg of a gas does 20,, kJ of work and receives 16 ,,kJ of heat when it is expanded between two st

English

Gujarati

Hindi

11.Thermodynamics

hard

$1 \,\,kg$ of a gas does $20\,\, kJ$ of work and receives $16 \,\,kJ$ of heat when it is expanded between two states. $A$ second kind of expansion can be found between the initial and final state which requires a heat input of $9\,\, kJ$. The work done by the gas in the second expansion is ....... $kJ$

A

$32$

B

$5$

C

$- 4$

D

$13$

Solution

For first kind of expansion

$\Delta W=20 \mathrm{KJ}$

$\Delta Q=16 \mathrm{KJ}$

$\therefore \Delta U=\Delta Q-\Delta W=-4 K J$

since, $U$ is a state function. Therefore, value of $DU$ in both expansions remain same.

Thus, for second expansion $:-$

$\Delta U=-4 K J, \Delta Q=9 K J$

$\therefore$ By first law of the thermodynamics

$\Delta \mathrm{W}=\Delta \mathrm{Q}-\Delta \mathrm{U}=13 \mathrm{KJ}$

Standard 11

Physics

Share

Similar Questions

If an ideal gas is compressed isothermally. Which of the following statements is true?

easy

(KVPY-2021)

$Assertion :$ The heat supplied to a system is always equal to the increase in its internal energy.
$Reason :$ When a system changes from one thermal equilibrium to another, some heat is absorbed by it.

easy

(AIIMS-2017)

Find the amount of work done to increase the temperature of one mole of an ideal gas by $30^o\ C$ if it is expanding under the condition …. $J$

$V\propto {T^{\frac{2}{3}}}$ $[R = 1.99\ cal/mol-K]$

hard

An ideal monoatomic gas is taken through the thermodynamic states $A \to B \to C \to D$ via the paths shown in the figure. If $U_A, U_B, U_C$ and $U_D$ represent the internal energy of the gas in state $A, B\, C$ and $D$ respectively, then which of the following is not true?

medium

$n$ mole a perfect gas undergoes a cyclic process $ABCA$ (see figure) consisting of the following processes.

$A \rightarrow B :$ Isothermal expansion at temperature $T$ so that the volume is doubled from $V _{1}$ to $V _{2}=2 V _{1}$ and pressure changes from $P _{1}$ to $P _{2}$

$B \rightarrow C :$ Isobaric compression at pressure $P _{2}$ to initial volume $V _{1}$

$C \rightarrow A$ : Isochoric change leading to change of pressure from $P _{2}$ to $P _{1}$

Total workdone in the complete cycle $ABCA$ is

hard

(JEE MAIN-2021)