A copper vat is 10 m long at room temperature (20 degrees C). How much

longer it is when it contains boiling water at 1 atm pressure?

Air in a balloon does 50 J of work while absorbing 70 J of heat. What is
its change in internal energy?

A bottle containing 3 kg of water at a temperature of 20 degrees C is placed
in a refrigerator where the temperature is kept at 3 degrees C. How much heat is transferred from the water to cool it to 3 degrees C?

Aluminum is melted during the recycling process.
(a) How much heat must be transferred to each kilogram of aluminum to bring it to its melting point, 660 degrees C, from room temperature, 20 degrees C?
(b) About how many cups of coffee could you make with this much heat?

A piston contains 1m^3 of helium at a temperature of 250 K and an absolute pressure of 1.0kPa. The following changes are made in sequence:
(a) First the volume of the piston is decreased to 0.2 m^3 while the temperature is kept constant, what is the pressure of the gas?
(b) Taking the gas after process (a) has been carried out. Now the volume of the gas is kept fixed at 0.2 m^3 but the temperature of the gas is raised to 500K. What does the pressure of the gas become?

We will be glad to review your work when shown any.

To solve these questions, we can use the principles of thermodynamics, specifically the laws of thermodynamics and the ideal gas law.

1. A copper vat is 10 m long at room temperature (20 degrees C). How much longer is it when it contains boiling water at 1 atm pressure?
To find the change in length of the copper vat, we need to consider the coefficient of linear expansion of copper. Copper has a linear expansion coefficient of approximately 0.000016 per degree Celsius.

The change in length can be calculated using the formula:
Change in length = Initial length * Linear expansion coefficient * Change in temperature

In this case, the change in temperature is the difference between the boiling point of water (100 degrees Celsius) and room temperature (20 degrees Celsius).

2. Air in a balloon does 50 J of work while absorbing 70 J of heat. What is its change in internal energy?
According to the first law of thermodynamics, the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. Therefore, we can calculate the change in internal energy using the equation:
Change in internal energy = Heat added - Work done

In this case, the heat added is 70 J and the work done is -50 J, since the work done is negative when the system does work on its surroundings.

3. A bottle containing 3 kg of water at a temperature of 20 degrees C is placed in a refrigerator where the temperature is kept at 3 degrees C. How much heat is transferred from the water to cool it to 3 degrees C?
To calculate the heat transferred, we can use the equation:
Heat transferred = Mass of the substance * Specific heat capacity * Change in temperature

In this case, the mass of water is 3 kg and the change in temperature is the difference between the initial temperature (20 degrees Celsius) and the final temperature (3 degrees Celsius). The specific heat capacity of water is approximately 4,186 J/kg°C.

4. Aluminum is melted during the recycling process.
(a) How much heat must be transferred to each kilogram of aluminum to bring it to its melting point, 660 degrees C, from room temperature, 20 degrees C?
To calculate the heat transferred to melt aluminum, we can use the equation:
Heat transferred = Mass of the substance * Specific heat capacity * Change in temperature

In this case, the mass of aluminum is 1 kg, and the change in temperature is the difference between the melting point of aluminum (660 degrees Celsius) and the initial temperature (20 degrees Celsius). The specific heat capacity of aluminum is approximately 900 J/kg°C.

(b) About how many cups of coffee could you make with this much heat?
To determine how many cups of coffee could be made, we need to know the amount of heat required to make a cup of coffee. Let's assume it is 100 kJ, or 100,000 J. Once we have that value, we can calculate the number of cups using the equation:
Number of cups = Heat transferred / Heat required per cup

Divide the heat transferred by the heat required per cup to get the number of cups.

5. A piston contains 1 m^3 of helium at a temperature of 250 K and an absolute pressure of 1.0 kPa. The following changes are made in sequence:
(a) First, the volume of the piston is decreased to 0.2 m^3 while the temperature is kept constant. What is the pressure of the gas?
In this case, since the temperature is constant, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. Therefore, we can calculate the final pressure using the equation:
Initial pressure * Initial volume = Final pressure * Final volume

Solve for the final pressure using the given values.

(b) Taking the gas after process (a) has been carried out. Now the volume of the gas is kept fixed at 0.2 m^3, but the temperature of the gas is raised to 500 K. What does the pressure of the gas become?
In this case, since the volume is kept constant, we can use Charles's Law, which states that the volume and temperature of a gas are directly proportional at constant pressure. Therefore, we can calculate the final pressure using the equation:
Initial pressure * Initial temperature = Final pressure * Final temperature

Solve for the final pressure using the given values.