If the piston moves to reduce the initial volume 10 times, keeping the temperature constant, find the number of moles of gas contained in the cylinder, if the work done on the gas is 38,180 J.
How ΔU = 0 since the temperature remains constant, in an isothermal process one has to:Ī cylinder fitted with a moving piston contains an ideal gas at 127✬. The pressure P and the volume V are graphed in a diagram P-V as shown in the figure and the work done is equal to the area under the curve: To obtain the total work in an isothermal process, we integrate the expression for dW: How Adx is the precisely the volume variation dV, so: Well, the work done is calculated by integrating a small differential work, in which a force F produces a small dx offset: In the case of an isothermal process the product PV it's constant. The values of n and R are constant: n is the number of moles of the gas and R the constant of the gases.
The ideal gas equation of state is PV = nRT, which relates volume to pressure P and the temperature T. Suppose that the system in question is an ideal gas contained in the cylinder of a movable piston of area TO, which does work when its volume V change of V 1 to V 2. This is another way of expressing the conservation of energy in the system, presented through ΔU or change in energy, Q as the heat supplied and finally W, which is the work done by said system. To calculate the work done by a system when the temperature is constant, we must use the first law of thermodynamics, which states: It does not have the behavior of an ideal system like the Carnot engine, but thermodynamic principles are common.Ĭalculation of the work done in an isothermal process The movement of a piston inside the cylinder is transmitted to other parts of the car and produces movement. The isothermal stages are compression and expansion of a gas that is responsible for producing useful work.Ī car engine operates on similar principles. The Carnot cycle consists of four stages, two of which are precisely isothermal and the other two are adiabatic. It is an ideal machine because it does not consider processes that dissipate energy, such as viscosity of the substance that does the work, nor friction. The Carnot cycleĪ Carnot engine is an ideal machine from which work is obtained thanks to entirely reversible processes. Various operating principles are used in its design. To maintain the proper temperature, devices called thermostats. Automotive engines, refrigerators, as well as many other types of machinery, operate correctly in a certain temperature range. Melting ice is another common isothermal process, as is placing water in the freezer to make ice cubes. In this way, such a slow heat exchange occurs that the temperature remains constant. One way to make a process isothermal is to put the substance that will be the system under study in contact with an external thermal reservoir, which is another system with a large caloric capacity. The thermal energy required for a phase change to occur in a substance is called latent heat or heat of transformation. In such cases, the molecules of the substance readjust their position, adding or extracting thermal energy. These changes are the phase changes, when the substance changes from solid to liquid, from liquid to gas or vice versa. In a gas, there are situations in which a change in the system does not produce variations in temperature, but in physical characteristics. The isothermal process or isothermal is a reversible thermodynamic process in which the temperature remains constant.