The potential function as follows: u(x) = ₂x Find the expression for at temperature I when the above function increases linearly. (a) (b) 0 € 1 kg I 2 11 1 KI 14 - "(x) when the particle is placed in the region x20 is defined KI 24

A sealed container holding 0.500 kg of liquid nitrogen at its boiling point of 77.3 K is placed in a large room at 21.0°C. Energy is transferred from the room to the nitrogen as the liquid nitrogen boils into a gas and then warms to the room’s temperature. (a) Assuming the room’s temperature remains essentially unchanged at 21.0°C, calculate the energy transferred from the room to the nitrogen. (b) Estimate the change in entropy of the room. Liquid nitrogen has a latent heat of vaporization of 2.01 x 105 J/kg. The specific heat of N2 gas at constant pressure is c(N2) = 1.04 x 103 J/kg · K .

1) Consider a tank containing 1 m³ of water at 20 °C. The tank is perfectly insulated. There are two copper rods, which each have one end in the water and the other in a reservoir at a different temperature. The first rod is 1 m long and 0.1 m in diameter, and its other end is in a reservoir of liquid nitrogen at 77 K. The second rod is 0.5 m long and 0.05 m in diameter, and its other end is connected to a reservoir at 120 °C. After some time the water in the tank freezes. What is the temperature of the ice in the tank when it finally reaches steady state? [kcu = 400 W m-¹ K-¹] a) 0 °C b) -20 °C c) - 50 °C d) - 70 °C e) - 90 °C

Ex 51: The temperature of interstellar space has an average value of about 5 K. Find the rms speed of a proton in the space. [mp = 1.673 x 10 27 kg, kB = 1.38 x 10 23 J/K]

A workshop with well-insulated walls and containing 800 m of air at 305 K is heated at constant pressure (atmospheric). Consider air to be an ideal diatomic gas. (a) Determine the energy (in k) required to increase the temperature of the air in the building by 2.90°C. kJ (b) Determine the mass (in kg) this amount of energy could lift through a height 3.10 m. kg

In a certain particle accelerator, protons travel around a circular path of diameter 23.0 m in an evacuated chamber, whose residual gas is at 295 K and 1.00 * 10-6 torr pressure. (a) Calculate the number of gas molecules per cubic centimeter at this pressure. (b) What is the mean free path of the gas molecules if the molecular diameter is 2.00 * 10-8 cm?

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If the gravitational potential energy of the water is equal to the increase in the internal energy of the water, compute the change in its temperature (in Kelvin), if water drops from a height of 50 m. Assume no work is done on/by the water (C = 4184 J/kg K)

(a) It is difficult to extinguish a fire on a crude oil tanker, because each liter of crude oil releases 2.80 X 107 J of energy when burned. To illustrate this difficulty, calculate the number of liters of water that must be expended to absorb the energy released by burning 1.00 L of crude oil, if the water has its temperature raised from 20.0C to 100.0C, it boils, and the resulting steam is raised to 300.0C. (b) Discuss additional complications caused by the fact that crude oil has a smaller density than water.