Question

A 100 W light bulb is placed in a cylinder equipped with a moveable piston. The light bulb is turned on for 2.0×10−2 hour, and the assembly expands from an initial volume of 0.85 L to a final volume of 5.88 L against an external pressure of 1.0 atm.

a)Use the wattage of the light bulb and the time it is on to calculate ΔU in joules (assume that the cylinder and light bulb assembly is the system and assume two significant figures). Express your answer using two significant figures.

b) Calculate w. Express your answer using two significant figures.

c) Calculate q. Express your answer using two significant figures.

Answer 1

Wattage of bulb = 100 W = 100 J/s

time = 2.0 x 10^-2 hr

time = 2.0 x 10^-2 hr * (3600 s / 1 hr)

time = 72 s

(a) Change in internal energy, $\dpi{100} \small \Delta$ U = (wattage of bulb) * (time)

$\dpi{100} \small \Delta$U = (100 J/s) * (72 s)

$\dpi{100} \small \Delta$U = 7200 J

(b) Work = pressure * (initial volume - final volume)

work = (1.0 atm) * (0.85 L - 5.88 L)

work = -5.03 atm-L

work = -5.03 atm-L * (101.325 J / 1 atm-L)

work = -510 J     (negative sign indicates work is done by the system)

(c) According to first law of thermodynamics,

$\dpi{100} \small \Delta$U = q + w

where $\dpi{100} \small \Delta$ U is the change in internal energy = 7200 J

q = heat gained by system

w = work done on system = -510 J

substituting the values,

7200 J = q + (-510 J)

q = 7200 J + 510 J

q = 7700 J