A cylinder containing an ideal gas has a volume of 3.0 m³ and a pressure of 1.0 × 10⁵ Pa at a temperature of 300 K.The cylinder is placed against a metal block that is maintained at 900 K and the gas expands as the pressure remains constant until the temperature of the gas reaches 900 K.The change in internal energy of the gas is 9.0 × 10⁵ J.Find the change in entropy of the block associated with the heat transfer to the gas. A) 0 B) +670 J/K C) −1700 J/K D) −1100 J/K

Question

Quizplus · Accepted Answer

The change in entropy of the metal block is given by:

ΔS = Q/T

Where Q is the heat transferred to the gas, and T is the constant temperature of the metal block.

Using the first law of thermodynamics, we can relate the change in internal energy of the gas to the heat transferred:

ΔU = Q + W

Where W is the work done by the gas. Since the pressure remains constant, we have:

W = PΔV = 0

Thus, ΔU = Q, and we can find the heat transferred to the gas:

Q = 9.0 × 10^15 J

Substituting into the expression for ΔS, we get:

ΔS = Q/T = (9.0 × 10^15 J)/(900 K) = -10,000 J/K

Therefore, the change in entropy of the metal block associated with the heat transfer to the gas is -1700 J/K (choice C).

A Cylinder Containing an Ideal Gas Has a Volume of 3.0