1 **Thermodynamics Problem Set**Welcome to our educational resource on thermodynamics! Below are several problems that will test your understanding of gas laws, thermodynamic processes, and related principles.1. **Problem 1 (13.13)** **Problem Statement:** To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.872 cm in diameter is to be placed in a hole 1.870 cm in diameter in a metal at 22°C. To what temperature must the rivet be cooled if it is to fit in the hole? **Explanation:** This problem involves thermal contraction of metals. When the rivet is cooled, it will contract, allowing it to fit into the slightly smaller hole. To solve this, one would typically use the linear expansion formula and properties of the material involved (in this case, steel).2. **Problem 2 (13.24)** **Problem Statement:** In an internal combustion engine, air at atmospheric pressure and a temperature of about 20°C is compressed in the cylinder by a piston to \(\frac{1}{9}\) of its original volume (compression ratio = 9.0). Estimate the temperature of the compressed air, assuming the pressure reaches 40 atm. **Explanation:** This problem deals with the ideal gas law and adiabatic compression. Using the principles of adiabatic processes and the given compression ratio, the resulting temperature and pressure conditions can be calculated. The relationship between pressure, volume, and temperature needs to be taken into account.3. **Problem 3 (13.29)** **Problem Statement:** What is the pressure inside a 38.0-L container holding 105.0 kg of argon gas at 21.6ºC? **Explanation:** This question requires the application of the ideal gas law \( PV = nRT \). Convert the mass of argon gas to moles (using the molar mass of argon), temperature to Kelvin, and solve for pressure. 4. **Problem 4 (13.49)** **Problem Statement:** If the pressure in a gas is tripled while its volume is held constant, by what factor does \( v_{\text{r

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(13.13) To make a secure fit, rivets that are larger than the rivet the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.872 cm in diameter is to be placed in a hole 1.870 cm in diameter in a metal at 22°C. To what temperature must the rivet be cooled if it is to fit in the hole?