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

Answer:

(a) ΔU = 7.2x10²

(b) W = -5.1x10²

(c) q = 5.2x10²

Explanation:

From the definition of power (p), we have:

$p = \frac {\Delta W}{\Delta t} = \frac {\Delta U}{\Delta t}$ (1)

where, p: is power (J/s = W (watt)) W: is work = ΔU (J) and t: is time (s)  

(a) We can calculate the energy (ΔU) using equation (1):

$\Delta U = p \cdot \Delta t = 100 \frac{J}{s} \cdot 2.0\cdot 10^{-2} h \cdot \frac{3600s}{1h} = 7.2 \cdot 10^{2} J$  

(b) The work is related to pressure and volume by:

$\Delta W = -p \Delta V$

where p: pressure and ΔV: change in volume = V final - V initial      

$\Delta W = - p \cdot (V_{fin} - V_{ini}) = - 1.0 atm (5.88L - 0.85L) = - 5.03 L \cdot atm \cdot \frac{101.33J}{1 L\cdot atm} = -5.1 \cdot 10^{2} J$

(c) By the definition of Energy, we can calculate q:

$\Delta U = \Delta W + \Delta q$

where Δq: is the heat transfer

$\Delta q = \Delta U - \Delta W = 7.2 J - (-5.1 \cdot 10^{2} J) = 5.2 \cdot 10^{2} J$    

I hope it helps you!