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A gas is contained in a cylinder at a pressure of 1 atm and a temperature of 25°C. The cylinder is fitted with a piston that can be moved to change the volume. The gas is allowed to expand irreversibly to a final pressure of 0.5 atm, and the temperature is kept constant. Calculate the work done by the system, and determine if the process is endothermic or exothermic.

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To calculate the work done by the system, we can use the formula for work done during an isothermal process:W = -nRT * ln V2/V1 where W is the work done, n is the number of moles of gas, R is the ideal gas constant  8.314 J/ molK  , T is the temperature in Kelvin, and V1 and V2 are the initial and final volumes, respectively.First, we need to convert the temperature from Celsius to Kelvin:T = 25C + 273.15 = 298.15 KSince the pressure is halved and the temperature is constant, the volume must double according to Boyle's Law  P1V1 = P2V2 :V2 = 2V1Now we can calculate the work done:W = -nRT * ln V2/V1  = -nRT * ln 2 However, we don't have the number of moles  n  given in the problem. To find the work done by the system, we can express the work done in terms of the initial and final pressures and volumes:W = -nRT * ln 2  = -nR *  298.15 K  * ln 2 Since we don't have the value of n, we cannot find the exact numerical value for the work done. However, we can see that the work done is negative, which means the system is doing work on the surroundings.As for whether the process is endothermic or exothermic, we need to consider the heat transfer during the process. Since the temperature remains constant during the process, the internal energy of the system does not change. According to the first law of thermodynamics:U = Q - WSince U = 0  due to constant temperature , we have:Q = WSince the work done is negative  W < 0 , the heat transfer  Q  must also be negative. This means that heat is being released by the system to the surroundings, making the process exothermic.

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