. When 2 moles of helium gas expand at constant pressure P = 1.0 × 105 Pascals, the temperature increases from 2℃ to 112℃. If the initial volume of the gas was 45 liters. Cp=20.8J/mol. K, Cv=12.6J/mol. K. Determine i. The work done W by the gas as it expands (4) ii. The total heat applied to the gas (2) iii. The change in internal energy (2

i. Work done by the gas as it expands is approximately 1,900 J

ii. The total heat supplied is approximately 4, 576 J

iii. The change in internal energy is approximately 2,772 J

Explanation:

The constant pressure of the helium gas, P = 1.0 × 10⁵ Pa

The initial and final pressure of the gas, T₁, and T₂ = 2°C (275.15 K) and 112°C (385.15 K) respectively

The number of moles of helium in the sample of helium gas, n = 2 moles

The volume occupied by the gas at state 1, V₁ = 45 L

i. By ideal gas law, we have;

P·V = n·R·T

Therefore;

Plugging in the values gives;

Where;

V₂ = The volume of the gas at state 2

Therefore;

The volume of the gas at state 2, V₂ ≈ 0.064 m³ = 64 Liters

Work done by the gas as it expands, W = P × (V₂ - V₁)

∴ W ≈ 1.0 × 10⁵ Pa × (64 L - 45 L) = 1,900 J

Work done by the gas as it expands, W ≈ 1,900 J

ii. The total heat supplied, Q = Cp·n·ΔT

∴ Q = 20.8 J/(mol·K) × 2 moles × (385.15 K - 275.15 K) = 4,576 J

The total heat supplied, Q = 4, 576 J

iii. The change in internal energy, ΔU = Cv·n·ΔT

∴ ΔU = 12.6 J/(mol·K) × 2 moles × (385.15 K - 275.15 K) = 2,772 J

The change in internal energy, ΔU = 2,772 J

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: