An ideal gas is taken through a cyclic thermodynamic process thro… - Vidyadip

Question

An ideal gas is taken through a cyclic thermodynamic process through four steps. The amount of heat involved in these steps are Q₁ = 5960J, Q₂ = -5585J. Q₃ = -2980J and Q₄ = 3645 respectively. The corresponding quantities of work involved are W₁= 200J, W₂ = -825J, W₃ = -1100J and W₄ respectively. Find the value of W₄. What is the efficiency of the cycle?

✓

Answer

As the process is cyclic, therefore, $\Delta\text{U}=0$
According to first law of thermodynamics $\Delta\text{Q}=\Delta\text{U}+\Delta\text{W}=\Delta\text{W}$
$\Delta\text{W}=\Delta\text{Q}$ or $\text{W}_1+\text{W}_2+\text{W}_3+\text{W}_4$ $=\text{Q}_1+\text{Q}_2+\text{Q}_3+\text{Q}_4$
$\text{W}_4(\text{Q}_1+\text{Q}_2+\text{Q}_3+\text{Q}_4)-(\text{W}_1+\text{W}_2+\text{W}_3)$
$=(5960-5585-2980+3645)\\-(-200-825-1100)$
$=1040-275=765\text{J}$
$\text{Effeciency}=\frac{\text{Net work done}}{\text{total heat absorbed}}$ $=\frac{\text{W}_1+\text{W}_2+\text{W}_3+\text{W}_4}{\text{Q}_1+\text{Q}_4}$
$\eta=\frac{2200-825-1100+765}{5960+3645}=\frac{1040}{9605}=0.1083$
$\eta=0.1083\times100\%=10.83\%$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Thermodynamics→Thermodynamics — all question types→Physics STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Displacement versus time curve for a particle executing S.H.M. is shown in Fig. Identify the points marked at which,

Velocity of the oscillator is zero,
Speed of the oscillator is maximum.

Two small bodies of masses 10kg and 20kg are kept a distance 1.0m apart and released, Assuming that only mutual gravitational forces are acting, find the speeds of the particles when the separation decreases to 0.5m.

A block of mass 30.0kg is being brought down by a chain. If the block acquires a speed of 40.0cm/s in dropping down 2.00m, find the work done by the chain during the process.

A solid cylinder of mass 20kg rotates about its axis with angular speed 100rads^-1. The radius of the cylinder is 0.25m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

Two particles of masses m₁ and m₂ are joined by a light rigid rod of length r. The system rotates at an angular speed co about an axis through the centre of mass of the system and perpendicular to the rod. Show that the angular momentum of the system is $\text{L}=\mu\text{r}^2\omega$ where $\mu$ is the reduced mass of the system defined as $\mu=\frac{\text{m}_1\text{m}_2}{\text{m}_1+\text{m}_2}.$

Explain clearly, with examples, the distinction between :
(a) magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval;
(b) magnitude of average velocity over an interval of time, and the average speed over the same interval.
[Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first. When is the quality sign true? [For simplicity, consider one-dimensional motion only].

Determine a unit vector which is perpendicular to both $\vec{\text{A}}=2\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{B}}=\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}.$

A uniform rod of length l is suspended by an end and is made to undergo small oscillations. Find the length of the simple pendulum having the time period equal to that of the rod.

A highway motorist travels at a constant velocity of 45km/ h^-1 in a 30km/ h^-1 zone. A motor-cyclist police officer has been watching from behind a bill board and at the same moment the speeding motorist passes the bill board, the police officer accelerates uniformly from rest to overtake her. If the acceleration of the police officer is 10km/ h^-2, how long does he take to reach the motorist?

The current through a wire depends on time as $\text{i}=\text{i}_0+\alpha\text{t},$
Where $\text{i}_0=10\text{A}$ and $\alpha=4\text{A/ s}.$ Find the charge that crosses through a section of the wire in 10 seconds.