A)2.00 g of helium gas at 100 ° C and a pressure of 1.00 atm expand in an isobar process so that the volume of the gas doubles. Helium is a monatomic gas with a molar mass of 4.00 g per mole.
Find the following:
1.the temperature of the gas after expansion
2. work performed on the gas
3.the heat added to the gas
4.the change in the internal energy of the gas
B) Your mug contains 300 ml of coffee at 90 ° C. The coffee is too hot to drink. You decide to cool the coffee by dropping ice cubes at -20 ° C in the coffee. How many grams of ice do you need to add to the coffee to cool it down to 60 ° C?
C) Make a simplified sketch of a thermal power machine where sizes W, Qh and Qc are included. Define the sizes and write down the expression for the efficiency of the thermal power machine.
D) A Carnot thermal power machine works between 500 ° C and 100 ° C. The Carnot machine is supplied with 250 J in each cycle. Find the efficiency of the Carnot machine. How many cycles does the machine have to go through to lift a stone with a mass of 500 kg to a height of 100 m?
E) Find the entropy change for each of the reservoirs in the Carnot machine (D) for single cycle. What is the entropy change of the universe for this cycle? Comment on the answer.
Task 2
A) In Figure 1 we see a point charge of + 2.00nC. Two circles are drawn around the point charge. The charge is located in the center of these dotted circles. The innermost has a radius equal to 1.00cm, and the outer has a radius equal to 2.00cm. On the innermost circle there are drawn in points A and B. On the outermost circle there is drawn in point C.
1.Find the electrical potential at points A, B and C
2. Find the electrical potential energy of an electron if the electron is placed in points A, B and C, respectively.
3. What is the potential difference between points A and B and the potential difference between points B and C?
4. Sketch electric field lines and equipotential surfaces around the charge
A metal rod with length L = 30.0 cm moves in a magnetic field Binn with size 0.450 T. The magnetic field Binn points inside the side (gray area), as shown in figure 2. The rod moves with velocity v = 5.00 ms^-1 in the negative y-direction as shown in the figure. Ignore gravity.
B) Derive the equation for the potential difference over the rod and the calculated number value of this. Which point, a or b, is at the highest potential? Explain your answer.
Task 3
show that two long, straight, and parallel conductors conducting direct current in the same direction attract each other.
Two circuits are shown in Figure 3. Both circuits contain resistors, capacitors, and coils. The values of resistor R, capacitance and inductance are the same in both circuits. Each circuit contains an AC voltage source. These sources are identical with same frequency and rms voltage. Frequency to AC voltage sources are very small. In which circuit does the AC power source provide the largest rms current? Explain your answer.
A coil with 10 windings lies in a magnetic fieldB with size 1.0 mT which points in the positive y-direction, as shown in figure 4. The coil has an end diameter of 1.0 cm and a resistance of 0.20 .The coil is connected to an uncharged capacitor with a capacitance of 1.0 μF. The coil is quickly pulled to the right (x-direction) out of the magnetic field.
Find the direction of the induced current, as well as the voltage induced across