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# Physics Problems: Sample Questions

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Consider a hot air-balloon. The deflated balloon, gondola, and 2 passengers have a combined mass of 315 kg. When inflated, the balloon contains 871m^3 of hot air. Find the temperature (degrees C) of the hot air required to lift the balloon off the ground. The air outside the balloon has a temperature of 20.2 degrees C and a pressure of 0.916x10^5 Pa. The pressure of the hot air inside the balloon is the same as the pressure of the air outside the balloon. The molar mass of air is 29g/mol. Hint: First find the density of the air outside the balloon. Then use Archimedes' principle to find the density required for the air inside the balloon. Then find the temperature of the air inside the balloon.

We drop a cube of ice into a glass of water. The mass of the cube of ice is 33.1 g and its initial temperature is -10.2 degrees C. The mass of the water is 251 g and its initial temperature is 19.7 degrees C. What is the final temperature (degrees C) of the water after all the ice has melted? Neglect any flow of heat to or from the environment. Give the answer to 2 significant figures. Now, repeat the previous problem using 90.0 g of ice. This time, not all of the ice will melt. (a) What is the final temperature (degrees C) of the water-ice mixture? (b) How much ice (g) is left?

We have some gas in a container at high pressure. The volume of the container is 420 cm^3. The pressure of the gas is 2.52x10^5 Pa. We allow the gas to expand at constant temperature until its pressure is equal to the atmospheric pressure, which at the time is 0.857x10^5 Pa. (a) Find the work (J) done on the gas. (b) Find the change of internal energy (J) of the gas. (c) Find the amount of heat (J) we added to the gas to keep it at constant temperature. Be sure to include the correct signs on the answers.