Temperature, heat and the first law of thermodynamics

Determine the temperature at which a thermometer in degrees Celsius and one in degrees Fahrenheit read the same number, and express it in kelvins.

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A bridge has a steel structure ($\alpha =1.2\cdot 10^{-5}{\mathrm{K}}^{-1}$) $200\mathrm{m}$ long at a temperature of $-10{}^{\circ }\mathrm{C}$. Compute the elongation of the structure when the temperature rises to $40{}^{\circ }\mathrm{C}$.

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A tank contains $50.0\mathrm{L}$ of gasoline ($\beta =9.5\cdot 10^{-4}{\mathrm{K}}^{-1}$) at a temperature of $10{}^{\circ }\mathrm{C}$. Neglecting the expansion of the tank, compute the increase in volume of the gasoline when the temperature rises to $30{}^{\circ }\mathrm{C}$.

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An electric kettle with a power of $2000\mathrm{W}$ heats $1.5\mathrm{kg}$ of water from $15{}^{\circ }\mathrm{C}$ to $100{}^{\circ }\mathrm{C}$. Assuming that all the electrical energy is absorbed by the water, compute the heat required and the time taken ($c_a=4186J/(\mathrm{kg}\cdot \mathrm{K})$).

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A piece of iron of mass $0.25\mathrm{kg}$ at a temperature of $200{}^{\circ }\mathrm{C}$ is immersed in $1.0\mathrm{kg}$ of water at $20{}^{\circ }\mathrm{C}$, in an insulated container of negligible heat capacity. Compute the equilibrium temperature ($c_{\mathrm{Fe}}=450J/(\mathrm{kg}\cdot \mathrm{K})$, $c_a=4186J/(\mathrm{kg}\cdot \mathrm{K})$).

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We want to cool $0.30\mathrm{kg}$ of a drink, which can be treated as water, from $25{}^{\circ }\mathrm{C}$ to $5.0{}^{\circ }\mathrm{C}$ by adding ice at $0{}^{\circ }\mathrm{C}$. Neglecting exchanges with the outside, compute the mass of ice needed ($c_a=4186J/(\mathrm{kg}\cdot \mathrm{K})$, ${\lambda }_f=3.33\cdot 10^{5}J/kg$).

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Compute the heat needed to bring to the boil and completely evaporate $0.500\mathrm{kg}$ of water initially at $20{}^{\circ }\mathrm{C}$, at atmospheric pressure ($c_a=4186J/(\mathrm{kg}\cdot \mathrm{K})$, ${\lambda }_v=2.26\cdot 10^{6}J/kg$).

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The glass of a window has area $1.5{\mathrm{m}}^2$, thickness $4.0\mathrm{mm}$ and thermal conductivity $k=0.80W/(\mathrm{m}\cdot \mathrm{K})$. Its two faces are at temperatures that differ by $2.0\mathrm{K}$. Compute the power lost by conduction.

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A room measures $5.0\mathrm{m}\times 4.0\mathrm{m}\times 3.0\mathrm{m}$ and contains air at $1.013\cdot 10^5\mathrm{Pa}$ and $20{}^{\circ }\mathrm{C}$. Treating air as an ideal gas with molar mass $29g/mol$, compute the number of moles and the mass of the air.

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$3.00\mathrm{mol}$ of diatomic ideal gas are heated at constant pressure and their temperature increases by $50.0\mathrm{K}$. Compute the heat absorbed, the work done by the gas and the change in internal energy.

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$1.00\mathrm{mol}$ of ideal gas at a temperature of $27.0{}^{\circ }\mathrm{C}$ is compressed quasi-statically and isothermally from a volume of $20.0\mathrm{L}$ to a volume of $10.0\mathrm{L}$. Compute the work done by the gas and the heat exchanged.

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A monatomic ideal gas at a temperature of $400\mathrm{K}$ expands adiabatically and quasi-statically until its volume doubles. Compute the final temperature and the ratio of the final pressure to the initial one.

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An ideal gas goes through the triangular cycle $A\to C\to B\to A$ with $A$ ($1.00\mathrm{L}$; $1.00\cdot 10^5\mathrm{Pa}$), $C$ ($1.00\mathrm{L}$; $3.00\cdot 10^5\mathrm{Pa}$) and $B$ ($3.00\mathrm{L}$; $1.00\cdot 10^5\mathrm{Pa}$), where each side is traversed quasi-statically along a segment of the $(V,p)$ plane. Compute the total work and the total heat exchanged in the cycle.

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