Question

1. A 370-mL spherical flask contains 0.065 mol of an ideal gas at a temperature of 283 K. What is the average force exerted on the walls of the flask by a single molecule?

2. A 4.9-kg block of ice at -1.5 ∘C slides on a horizontal surface with a coefficient of kinetic friction equal to 0.069. The initial speed of the block is 7.2 m/s and its final speed is 5.5 m/s. Assuming that all the energy dissipated by kinetic friction goes into melting a small mass m of the ice, and that the rest of the ice block remains at -1.5 ∘C, determine the value of m (kg).

Answer 1

1) P = n∙R∙T/V
= 0.065 mol * 8.3145 J∙mol⁻¹∙K⁻¹ * 283K / (370×10⁻⁶ m³)
P = 41334 Pa

V = (1/6)∙π∙D³

D = (6∙V/π) ^1/3

A = pi/4 * (6∙V/π) ^2/3

A = 6.231*10^-3 m2

F = 41334 *6.231*10^3 =257.55 N

of force is applied by 0.065 mol = 0.065*6.023*10^23 molecules

Average force = F/molecules = 6.578*10^-21 N

2) m = 4.9kg, N = 4.9g

f = 0.069*4.9*9.81

a= -0.069*9.81 = 0.676 m/s2

v = 5.5 m/s, u = 7.2 m/s

t = 5.5-7.2/-0.676 = 2.51s

F = 4.9*0.676 = 3.314J

distance travelled is 7.2^2 - 5.5^2 = 2*0.676*s

s = 15.97m

Power = 3.314*15.97 = 52.92 W

heat from ice = m(334000 + 1.5*2100) = 52.92

m = 0.157 g