Question

Five moles of a monatomic ideal gas in a cylinder at 27°C is expanded isothermally from a volume of 5 L to 10 L.

(a) What is the change in internal energy?
(b) How much work was done on the gas in the process?
(c) How much heat was transferred to the gas?

Answer 1

The change in internal energy is 0 J, the work done on the gas is 0 J, and the heat transferred to the gas is 0 J.

Step-by-step explanation:

(a) The change in internal energy of an ideal gas undergoing an isothermal expansion can be calculated using the equation ΔU = 0, since the internal energy of an ideal gas only depends on temperature. So, the change in internal energy is zero.

(b) The work done on the gas in an isothermal expansion can be calculated using the equation W = nRT ln(Vf/Vi), where n is the number of moles of the gas, R is the ideal gas constant, T is the temperature, and Vf and Vi are the final and initial volumes, respectively. Plugging in the given values, we get W = 5 x 8.314 x 300 x ln(10/5) = 0 J.

(c) The heat transferred to the gas in an isothermal expansion is equal to the work done on the gas, since the internal energy remains constant. Therefore, the heat transferred to the gas is also 0 J.