Suppose 2400 J of heat are added to 4.2 mol of argon gas at a constant pressure

Question

Suppose 2400 J of heat are added to 4.2 mol of argon gas at a constant pressure of 120 kPa. (Assume that the argon can be treated as an ideal monatomic gas.) (a) Find the change in internal energy. J (b) Find the change in temperature for this gas. K (c) Calculate the change in volume of the gas. m3

Explanation / Answer

Q Physics - Change in Internal Energy, Temperature, and Volume? Suppose 1900 J of heat are added to 2.4 mol of argon gas at a constant pressure of 120 kPa. (Assume that the argon can be treated as an ideal monatomic gas.) (a) Find the change in internal energy. Answer in J (b) Find the change in temperature for this gas. Answer in K (c) Calculate the change in volume of the gas. ans (a) The heat transferred in a constant pressure process equals the change in enthalpy: ?H = Q Change in enthalpy and internal energy for an ideal gas are given by: ?H = n·Cp·?T ?U = n·Cv·?T The molar heat capacities at constant pressure and constant volume for a monatomic ideal gas are: Cp = (5/2)·R Cv = (3/5)·R Hence, ?H = (5/2)·n·R·?T ?U = (3/2)·n·R·?T When you compare the two relations you find ?U = (3/5)·?H Hence, ?U = (3/5)·Q = (3/5)·1900J = 1140 J (b) ?U = (3/2)·n·R·?T => ?T = 2·?U /(3·n·R) = 2 · 1140J / (3 · 2.4 mol · 8.3145J/Kmol) = 38K (c) p·V = n·R·T => V = n·R·T/p Since n,R and p are constants: ?V = n·R·?T /p = (2/3)·?U /p = (2/3) · 1140 J / 120×10³ Pa = 6.33×10?³ m³

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