# work done on the system example

Here the work-energy theorem can be used, because we have just calculated the net work $$W_{net}$$ and the initial kinetic energy, $$\frac{1}{2}mv_0^2$$ These calculations allow us to find the final kinetic energy, $$\frac{1}{2}mv^2$$ and thus the final speed $$v$$. The enthalpy change for the following reaction is – 620 J, when 100 mL of ethylene and 100 mL of H2 react at 1 atm pressure. Let us start by considering the total, or net, work done on a system. Given: q = + 6 kJ (Heat absorbed), W = -1.5 kJ (Work done on the surroundings). Thus, as expected, the net force is parallel to the displacement, so that $$\theta = 0$$ and $$cos \, \theta = 1$$, and the net work is given by, The effect of the net force $$F_{net}$$ is to accelerate the package from $$v_0$$ to $$v$$ The kinetic energy of the package increases, indicating that the net work done on the system is positive.

We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Calculate the work done in the following reaction when 2 mol of NH4NO3 decomposes at constant pressure at 10o °C. An ideal gas expands from a volume of 6 dm³ to 16 dm³ against constant external pressure of 2.026 x 105 Nm-2.

Calculate the work done in the following reaction when 2 moles of HCl are used at constant pressure and 423 K. State whether work is on the system or by the system. To reduce the kinetic energy of the package to zero, the work $$W_{fr}$$ by friction must be minus the kinetic energy that the package started with plus what the package accumulated due to the pushing.

Unit of work done in any system of units is equal to the unit of force multiplied by the unit of distance. Calculate the work done in the following reaction when 1 mol of SO2 is oxidised at constant pressure at 5o °C.

We know that once the person stops pushing, friction will bring the package to rest. The net work on a system equals the change in the quantity $$\frac{1}{2}mv^2$$. We will also develop definitions of important forms of energy, such as the energy of motion. We will now consider a series of examples to illustrate various aspects of work and energy. In this case, $$F \, cos \, \theta$$ is constant. In terms of energy, friction does negative work until it has removed all of the package’s kinetic energy. Figure (a) shows a graph of force versus displacement for the component of the force in the direction of the displacement—that is, an $$F \, cos \, \theta$$ vs. $$d$$ graph. Does the transfer of energy take place when you push a huge rock with all your might and fail to move it? is the energy associated with translational motion.

Steps. The forces acting on the package are gravity, the normal force, the force of friction, and the applied force. In general, if a strong force causes an object to move very far, a lot of work is done, and if the force is small or the object doesn't move very far, only a little work is done. \]. Where is the energy you spend going? What are the change in internal energy and enthalpy change of the system? From given reaction 2 x (12 + 16) = 56 g of CO on oxidation liberates  566 kJ energy, Hence heat liberated on oxidation of 7.0 g of CO = (7.0/56) × 566 = 70.75 KJ, Hence ΔH = – 70.75 kJ (negative sign as heat is liberated), ∴ Δ U = 0.2836 kJ – 70.75 kJ =  -70.47 kJ, Ans: The work done on the system is 0.2836 kJ and Δ U = -70.47 kJ. How far does the package in Figure 7.03.2. coast after the push, assuming friction remains constant?

In this section we begin the study of various types of work and forms of energy. (b) Solve the same problem as in part (a), this time by finding the work done by each force that contributes to the net force. Kinetic energy is a form of energy associated with the motion of a particle, single body, or system of objects moving together. The initial pressure is 3 bar, the initial volume is 0.1 m3, and the final volume is 0.2 m3. Teachoo is free. Example $$\PageIndex{2}$$: Determining the Work to Accelerate a Package. Find Enthalpy change if ΔU is 418 J. (c) Work done is zero :- Force is at right angle to the displacement for example work of a centripetal force on a body moving in a circle. This fact is consistent with the observation that people can move packages like this without exhausting themselves. In SI system unit of work is 1Nm and is given a name Joule(J). Using work and energy, we not only arrive at an answer, we see that the final kinetic energy is the sum of the initial kinetic energy and the net work done on the package. Note that the unit of kinetic energy is the joule, the same as the unit of work, as mentioned when work was first defined. This expression is called the work-energy theorem, and it actually applies in general (even for forces that vary in direction and magnitude), although we have derived it for the special case of a constant force parallel to the displacement. Thus, $d' = -\dfrac{W_{fr}}{f} = \dfrac{-95.75 \, J}{5.00 \, N},$. Thus the net work is, $W_{net} = F_{net}d = (115 \, N)(0.800 \, m)$. Thus, 1J=1Nm In CGS system unit is erg Learn Science with Notes and NCERT Solutions, Next: Work done by body Moving in Circular Direction→, Work Done By Force Acting Obliquely (Indirectly), Work done by body Moving in Circular Direction, Conservation of Energy in Simple Pendulum, Direction of force and Direction of Motion are at right angle (angle of 90 degrees), Force is applied but there is no displacement. The person actually does more work than this, because friction opposes the motion. Have questions or comments? We will see in this section that work done by the net force gives a system energy of motion, and in the process we will also find an expression for the energy of motion. \], Solving for the final speed as requested and entering known values gives, $v = \sqrt{\dfrac{2(95.75 \, J)}{m}} = \sqrt{\dfrac{191.5 \, kg \cdot m^2/s^2}{30.0 \, kg}}$. CO reacts with O2 according to the following reaction. He provides courses for Maths and Science at Teachoo. c) Suppose that as the original sample absorbs heat, it expands against atmospheric pressure and does 600 kJ of work on its surroundings. ΔH = qp = Heat supplied at constant pressure = + 6 kJ, Ans: The change in internal energy is 4.5 kJ and enthalpy change is 6 kJ. The calculated total work $$W_{total}$$ as the sum of the work by each force agrees, as expected, with the work $$W_{net}$$ done by the net force. The work done is e $$(F \, cos \, \theta)_{i(ave)}d_i$$ for each strip, and the total work done is the sum of the $$W_i$$. On the whole, solutions involving energy are generally shorter and easier than those using kinematics and dynamics alone. Suppose that you push on the 30.0-kg package in Figure 7.03.2. with a constant force of 120 N through a distance of 0.800 m, and that the opposing friction force averages 5.00 N. (a) Calculate the net work done on the package. In equation form, the translational kinetic energy. is done.

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Force can be calculated with the formula Work = F × D × Cosine(θ), where F = force (in newtons), D = displacement (in meters), and θ = the angle between the force vector and the direction of motion. Sign convention: work done by a system is positive, and the work done on a system is negative. Example $$\PageIndex{3}$$: Determining Speed from Work and Energy. negative work

Explain your answer. The work-energy theorem states that the net work $$W_{net}$$ on a system changes its kinetic energy, $$W_{net} = \frac{1}{2}mv^2 - \frac{1}{2}mv_0^2$$. What is the work done by the force of gravity on the object? This quantity is our first example of a form of energy. If the line joining A and B is horizontal, what is the work done on the object by the gravitational force? Ans: Work done by the surroundings on the system in the reaction is – 18.61 kJ. Use work and energy considerations.

NCERT Question 5 - What happens to the work done on a system?

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