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Configurational Entropy
Ludwig Boltzmann killed himself so that we could do thermodynamics by enumerating the states of a system. Learn to count, the most important skill in statistical mechanics.
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A \( 7.0 \text{ kg} \) sample of metal with a specific heat of \( 0.2 \text{ kJ/kg}^\circ\text{C} \) is supplied with \( 42.0 \text{ kJ} \) of heat and has its temperature raised to \( 48.0 ^\circ \text{C} .\) Find the initial temperature of the metal.
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If helium gas fills a spherical balloon of radius \(16.0 \text{ cm}\) at \(25.0 ^\circ\text{C}\) and \(1.013 \times 10^5 \text{ N/m}^2,\) what is the approximate total kinetic energy of the helium atoms in the balloon?
The value of the Boltzmann constant \(k_B\) is \(1.38 \times 10^{-23} \text{ J/K}\) and the value of the universal gas constant \(R\) is \(8.31 \text{ J/mol}\cdot\text{K}.\)
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If the temperature of a liquid is increased by \( 10 ^\circ \text{C}, \) its density decreases by \( 2 \%. \) Find the coefficient of volume expansion of the liquid.
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Assume that we have found a new multicellular species. During the research of that species, it is found that one cell has \( 300,000 \) base pairs of DNA. If a single individual of the new species has about \( 25,000 \) cells, what is the total number of base pairs of DNA in its whole body?
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