Question

An ideal gas undergoes isothermal compression from an initial volume of 4.81 m^3 to a final volume of 2.78 m^3. There is 7.25 mol of the gas, and its temperature is 23.1°C. (a) How much work is done by the gas? (b) How much energy is transferred as heat between the gas and its environment?

Answer 1

a) W = - 9785.03 J

b) 9785.03 J is transferred to the environment.

Step-by-step explanation:

n = 7.25 mol be the number of moles of the gas, T = 23.1 + 273 = 296.1 K be the temperature of the gas, Vf = 2.78 m^3 be the final volume of the gas, Vi = 4.81 m^3 be the volume of the gas.

a) The work done on compressing the gas is:

W = n×R×T×ln(Vf/Vi)

= (7.25)×(8.314)×(296.1)×ln(2.78/4.81)

W = - 9785.03 J

Therefore, the work done on compressing the gas is - 9785.03 J.

b) given the internal energy change is ΔEint vanishes when ΔT = 0, the heat transferred to the environment is found by considering the fact that from the first law of thermodynamics, Q = W = -9785.03 J so 9785.03 J is transferred to the environment.