Question

A balloon filled with 39.1 moles of helium has a volume of 876 l at 0.0'c and 1.00 atm pressure. the temperature of the balloon is increased to 38.0'c as it expands to a volume of 998 l, the pressure remaining constant. calculate q, w, and #e for the helium in the balloon. (the molar heat capacity for helium gas is 20.8 j/°c # mol.)

Answer 1

Q = 30.90 kJ, W = 12.36 kJ, ΔE = 18.54 kJ.

Step-by-step explanation:

The expansion is happening at constant pressure without a phase change, thus, the heat can be calculated by:

Q = n*c*ΔT

Where n is the number of moles, c is the molar heat capacity, and ΔT is the temperature variation (final - initial), thus:

Q = 39.1*20.8*(38.0 - 0.0)

Q = 30904.64 J

Q = 30.90 kJ

The work done by a expansion at constant pressure is:

W = P*ΔV

Where P is the pressure (1 atm = 101325 Pa), and ΔV the volume variation (final - initial). Vfinal = 998 L = 0.998m³, Vinitial = 876 L = 0.876 m³.

W = 101325*(0.998 - 0.876)

W = 12361.65 J

W = 12.36 kJ

By the first law of the thermodynamics, the variation of the internal energy ΔE is:

ΔE = Q - W

ΔE = 30.90 - 12.36

ΔE = 18.54 kJ