Exam 18: A Macroscopic Description of Matter

The hole for a bolt in a brass plate has a diameter of 1.200 cm at 20°C.What is the diameter of the hole when the plate is heated to 220°C? The coefficient of linear thermal expansion for brass is 19 × 10^-6/°C.(Express your answer to 4 significant figures.)

Two identical concrete slabs lie flat and in contact with each other as shown in the figure.If the temperature increases by 40°C,the lower edges opposite the contact edges remained fixed in position,and the lower edges of the contact side remain in contact,at what angle will the slabs be tilted? The coefficient of thermal expansion of the concrete is 10 × 10^-6/K.

A fixed amount of ideal gas is held in a rigid container that expands negligibly when heated.At 20°C the gas pressure is p.If we add enough heat to increase the temperature from 20°C to 40°C,the pressure will be

Suppose that a steel bridge,1000 m long,was built without any expansion joints and that only one end of the bridge was held fixed.What would the difference in the length of the bridge be between winter and summer,taking a typical winter temperature as 0.00°C,and a typical summer temperature as 40°C? The coefficient of thermal expansion of steel is 10.5 × 10^-6 K^-1.

A hot air balloon has a volume of 2.00 × 10³ m³ when fully inflated,and the air inside the balloon is always at atmospheric pressure of 1.01 × 10⁵ Pa because of the large opening used to fill the balloon and heat the air inside it.What is the mass of hot air inside the balloon if its temperature is 120°C? The universal gas constant is 8.314 J/mol ∙ K.(Assume a molecular weight of 28.8 g/mol for air.)

Which contains more moles of material: 80 grams of helium gas (He,having atomic weight 4.0 g/mol)or 400 grams of argon gas (Ar,having atomic weight 40 g/mol)?

The figure shows a 50-kg frictionless cylindrical piston that floats on 0.68 mol of compressed air at 30°C.How far does the piston move if the temperature is increased to 300°C?

How many moles of water (H₂O)molecules are in a 4.00 m³ container at a pressure 8.00 × 10⁵ N/m² and temperature 600°C? The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K.

A vertical tube that is closed at the upper end and open at the lower end contains an air pocket.The open end of the tube is under the water of a lake,as shown in the figure.When the lower end of the tube is just under the surface of the lake,where the temperature is 37°C and the pressure is 1.0 × 10⁵ Pa,the air pocket occupies a volume of .Suppose now that the lower end of the tube is at a depth of 86 m in the lake,where the temperature is 7.0°C.What is the volume of the air pocket under these conditions? The density of the water in the lake is 1000 kg/m³.

A cold trap is set up to cause molecules to linger near the suction in a vacuum system.If the cold trap has an effective volume of 0.200 L and is maintained at how many molecules are in it at 10.0 Pa of pressure? (Avogadro's number is 6.022 × 10²³ molecules/mol,and the universal gas constant is 8.314 J/mol ∙ K.Assume the behavior of an ideal gas.)

A weather balloon contains 12.0 m³ of hydrogen gas when the balloon is released from a location at which the temperature is 22.0°C and the pressure is 101 kPa.The balloon rises to a location where the temperature is -30.0°C and the pressure is 20.0 kPa.If the balloon is free to expand so that the pressure of the gas inside is equal to the ambient pressure,what is the new volume of the balloon? Assume that in both cases the hydrogen gas is in thermal equilibrium with the outside air.

A glass flask has a volume of 500 mL at a temperature of 20°C.The flask contains of mercury at The temperature of the mercury and flask is raised until the mercury reaches the reference mark.The coefficients of volume expansion of mercury and glass are 18 × 10^-5 K^-1 and 2.0 × 10^-5 K^-1,respectively.The temperature at which this occurs is closest to

The figure shows a pV diagram for 0.0066 mol of gas that undergoes the process 1 → 2 → 3.What is the pressure p₂.The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K.

A sealed 26- tank is filled with 2000 moles of oxygen gas (O₂)at an initial temperature of 270 K.The gas is heated to a final temperature of 460 K.The ATOMIC mass of oxygen is 16.0 g/mol,and the ideal gas constant is R = 8.314 J/mol · K = 0.0821 L · atm/mol · K.The final pressure of the gas is closest to

A machinist needs to remove a tight fitting pin of material A from a hole in a block made of material B.The machinist heats both the pin and the block to the same high temperature and removes the pin easily.What statement relates the coefficient of thermal expansion of material A to that of material B?

The coefficient of linear expansion of aluminum is 24 × 10^-6 K^-1 and the coefficient of volume expansion of olive oil is 0.68 × 10^-3 K^-1.A novice cook,in preparation for deep-frying some potatoes,fills a 1.00-L aluminum pot to the brim and heats the oil and the pot from an initial temperature of 15°C to 190°C.To his consternation some olive oil spills over the top.How much?

A 3.2-L volume of neon gas (Ne)is at a pressure of 3.3 atm and a temperature of 330 K.The atomic mass of neon is 20.2 g/mol,Avogadro's number is 6.022 × 10²³ molecules/mol,and the ideal gas constant is R = 8.314 J/mol · K = 0.0821 L · atm/mol · K.The mass of the neon gas is closest to

A brass rod is 40.1 cm long and an aluminum rod is 79.3 cm long when both rods are at an initial temperature of 0°C.The rods are placed in line with a gap of 0.60 cm between them,as shown in the figure.The distance between the far ends of the rods is maintained at 120.0 cm throughout.The temperature of both rods is raised until the two rods are barely in contact.The coefficients of linear expansion of brass and aluminum are 2.0 × 10^-5 K^-1 and 2.4 × 10^-5 K^-1,respectively.The temperature at which contact of the rods barely occurs is closest to

The figure shows a pV diagram for 0.95 mol of gas that undergoes the process 1 → 2.The gas then undergoes an isochoric heating from point 2 until the pressure is restored to the value it had at point 1.What is the final temperature of the gas? The ideal gas constant is R = 8.314 J/mol ∙ K = .

Sometimes an experiment requires a certain pure gas to be used at reduced pressure.One way to achieve this is to purchase a sealed glass container filled with the gas,and to introduce the gas into a vacuum by attaching the glass container to the vacuum chamber and breaking the tip of the glass container using a metallic bean and a magnet.If the volume of the glass container is 1.0 L and it is at a pressure of 1.0 × 10⁵ Pa and if the vacuum chamber has a volume of 2.0 L,what will the pressure be after the gas,which is to be assumed to be an ideal gas,is released into the vacuum chamber and the temperature has returned to its original value? (Note that the glass container remains part of the system.)