A block of mass m = 0.2 kg slides across a rough horizontal surface with coefficient of kinetic friction $\mu$_k = 0.5. What is the change in entropy after the block has moved a distance of 1 m? The temperature of the block and surrounding is 22 $\circ$ C.

Question

Quizplus · Accepted Answer

The change in entropy can be calculated using the equation ΔS = -Q/T, where Q is the heat transferred during the process and T is the temperature. In this case, there is no heat transferred, so ΔS = 0, and the answer is E) zero.

Alternatively, the change in entropy can be calculated using the formula ΔS = -mukNln(d2/d1), where N is the normal force, d2 is the final position, and d1 is the initial position. The normal force N can be found using N = mg, and the distance d2 - d1 is 1 m. Plugging in the numbers, we get ΔS = -(0.2 kg)(0.5)(0.2 kg)(9.8 m/s^2)ln(2) = -3.3 J/K, which is closest to choice B). However, this calculation assumes that all the work done by the friction force is converted to heat, which may not be completely true in reality. Hence, the more accurate answer is still E) zero.

A Block of Mass M = 0 μ\muμ k = 0 ∘\circ∘

A Block of Mass M = 0 $\mu$ _k = 0 $\circ$