Thermal Properties Of Matter

the correct answer is: Volume.

Indeed, when a phase transition occurs, there is no increase in temperature.

When a square loop is formed from a wire with resistance and a voltage of 12 V is applied between two adjacent corners, we can consider the square as two resistors in series along one side of the square and two in series along the other side, forming two parallel paths from one corner to the opposite corner.
Step 1: Each side of the square has resistance . The total resistance between two adjacent corners (half the square) is: Step 2: The equivalent resistance between opposite corners (along the diagonal), with two such half resistances in parallel, is: Step 3: The current through the circuit, using Ohm's law ( ), is: Step 4: The voltage across the diagonal, where the resistance is , becomes:

Step 1: Recognize that the magnet's magnetic field and the Earth's magnetic field are combining to form a resultant field at the given point.
Step 2: Since the resultant field makes a angle with the Earth's magnetic field, the magnitudes of the Earth's field and the magnet's field at that point are equal. Thus: Step 3: Use the formula for the magnetic field due to a dipole at the midpoint of its perpendicular bisector: Where: - is the magnetic field at the point on the normal bisector, - is the magnetic moment of the magnet, - is the distance from the magnet to the point (here, ), - .
Step 4: Solve for (magnetic moment of the magnet):

Step 1: Understanding Internal Energy Change
For an ideal gas, the internal energy depends only on temperature and is given by: Since internal energy is a state function, the change in internal energy depends only on the initial and final temperatures, regardless of the process.
Step 2: Applying to Both Conditions
- When heated at constant volume: - When heated at constant pressure: Since depends only on , it is the same in both cases.
Step 3: Conclusion
Thus, the change in internal energy remains the same whether heating occurs at constant volume or constant pressure.

Step 1: Understanding Heat Transfer Through Composite Slabs
The heat transfer rate through a composite slab in steady-state condition is the same through both materials: where: - are the thermal conductivities of copper and brass, - , , - is the temperature at the interface.
Step 2: Applying Given Ratio
Given that the ratio of thermal conductivities is: Let and . Using the steady-state heat transfer equation: Step 3: Solving for Interface Temperature
Canceling and : Step 4: Conclusion
Thus, the temperature at the interface is:

Step 1: The activity of a radioactive substance is given by the formula: where is the decay constant and is the number of nuclei. For one mole of radium, is Avogadro's number ( ).
Step 2: The activity is given as kilo curie. We convert this into becquerels (1 kilo curie = Bq), so: Step 3: Now, using the formula for the decay constant:

For the disc to leave the surface of the hemisphere, the normal force must become zero at the point of leaving. Using the conservation of mechanical energy and Newton's laws, we can set the centripetal force required to keep the disc on the hemisphere equal to the gravitational component acting perpendicular to the surface at the point of leaving, which is at the very top of the hemisphere.
The required velocity for this to occur can be calculated by setting the gravitational force equal to the required centripetal force at the top, where is the mass of the disc: