The figure shows the $P-V$ plot of an ideal gas taken through a cycle $ABCDA.$ The part $ABC$ is a semicircle and $CDA$ is half of an ellipse. Then,
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For clockwise cycle on $p-V$ diagram with $P$ on $y$ $-axis,$ net work done is positive.
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A thermally insulated rigid container contains an ideal gas heated by a filament of resistance $100 \,\Omega$ through a current of $1\,A$ for $5$ min then change in internal energy is...... $kJ$
A closed vessel contains $0.1$ mole of a monoatomic ideal gas at $200\, K$. If $0.05$ mole of the same gas at $400\, K$ is added to it, the final equilibrium temperature (in $K$ ) of the gas in the vessel will be closed to
One mole of a monoatomic ideal gas $\left(c_{ V }=\frac{3}{2} R \right)$ undergoes a cycle where it first goes isochorically from the state $\left(\frac{3}{2} P _0, V _0\right)$ to $\left( P _0, V _0\right)$, and then is isobarically contracted to the volume $\frac{1}{2} V _0$. It is then taken back to the initial state by a path which is a quarter ellipse on the $P - V$ diagram. The efficiency of this cycle is
A hypothetical gas expands adiabatically such that its volume changes from $8$ litres to $27$ litres. If the ratio of final pressure of the gas to initial pressure of the gas is $\frac{16}{81}$. Then the ratio of $\frac{C_P}{C_V}$ will be
One mole of an ideal gas at $300 \mathrm{~K}$ in thermal contact with surroundings expands isothermally from $1.0 \mathrm{~L}$ to $2.0 \mathrm{~L}$ against a constant pressure of $3.0 \mathrm{~atm}$. In this process, the change in entropy of surroundings $\left(\Delta S_{\text {surr }}\right)$ in $\mathrm{J} \mathrm{K}^{-1}$ is $(1 \mathrm{~L} \mathrm{~atm}=101.3 \mathrm{~J})$
A monoatomic gas at pressure $P$ and volume $V$ is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be $.....P$