Multiple Choice
Which of the following conditions must be met for the entropy of a pure solid to be zero according to the Third Law of Thermodynamics?
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19. Chemical Thermodynamics
Third Law of Thermodynamics
Multiple Choice
A brand new deck of cards which hasn't been shuffled yet, possesses only one arrangement. Another, older deck has been shuffled and possesses 8 × 1067 arrangements. Calculate and compare entropies of each deck.
A
deck 1 = 0, deck 2 = 2.158 × 10−21 J/K
B
deck 1 = 0, deck 2 = 9.371 × 10−22 J/K
C
deck 1 = 0, deck 2 = 9.371 × 1024 J/K
D
deck 1 = 0, deck 2 = 2.158 × 1025 J/K
Verified step by step guidance1
Understand that entropy (S) is a measure of the disorder or randomness of a system. In this context, it relates to the number of possible arrangements (W) of the deck of cards.
Use the Boltzmann entropy formula: S = k * ln(W), where k is the Boltzmann constant (1.38 × 10^-23 J/K) and W is the number of arrangements.
For the brand new deck, which has only one arrangement, W = 1. Substitute W = 1 into the formula: S = k * ln(1). Since ln(1) = 0, the entropy S = 0 J/K.
For the shuffled deck, W = 8 × 10^67. Substitute this value into the formula: S = k * ln(8 × 10^67).
Calculate the natural logarithm of 8 × 10^67 and multiply by the Boltzmann constant to find the entropy of the shuffled deck. This will give you the entropy value in J/K.
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