Volume = πr²h = π(3²)(5) = 45π cubic units.

Volume = (4/3)πr³ = (4/3)π(5)³ = (4/3)π(125) = 500/3π cubic units.

Using the Rydberg formula, the wavelength for the transition from n=3 to n=1 can be calculated to be approximately 102.6 nm.

Using the Rydberg formula, the wavelength for the transition from n=4 to n=2 can be calculated to be approximately 486 nm.

Using the formula λ = d sin θ / m, where d = 0.1 mm, θ = 30°, and m = 1, we find λ = 0.1 mm * sin(30°) = 0.1 mm * 0.5 = 0.05 mm = 0.2 mm.

Work = F × d × cos(θ) = 15 N × 4 m × cos(60°) = 15 × 4 × 0.5 = 30 J.

Work done (W) = P * ΔV = 3 atm * (5 L - 2 L) = 3 atm * 3 L = 9 atm·L = 15 J (1 atm·L = 101.325 J)

Work done (W) = PΔV = P(V_final - V_initial) = 5 atm * (5 L - 2 L) = 15 L·atm.

The work done by an ideal gas during an isobaric (constant pressure) expansion is given by W = PΔV.

The work done during an isothermal expansion is given by W = nRT ln(V2/V1).

For an ideal gas undergoing isothermal expansion, the work done is given by W = nRT ln(Vf/Vi).

The work done on a gas during isothermal compression is positive, as work is done on the gas to compress it.

Work done (W) = P * ΔV = 2 atm * (2 L - 4 L) = 2 atm * (-2 L) = -4 L·atm (work done on the gas is positive).

Work done (W) = P * ΔV = 200 kPa * (2 L - 5 L) = 200 kPa * (-3 L) = -600 J (work done on the gas).

Work done = nRT ln(Vf/Vi) = 1 mol × 8.31 J/mol·K × 300 K × ln(20/10) = 1660 J.

Work done W = nRT ln(Vf/Vi) = 1 * 8.314 * 300 * ln(20/10) = 600 J.

Work done (W) = nRT ln(Vf/Vi) = 1 mol * 8.314 J/(mol K) * 300 K * ln(20/10) = 2.5 kJ.

Work done (W) = F × d = 50 N × 3 m = 150 J.

Work done (W) = Force × Distance = 10 N × 5 m = 50 J.

Work = Force * Distance * cos(θ) = 15 N * 3 m * cos(0°) = 45 J.

W = F × d × cos(θ) = 15 N × 3 m × cos(60°) = 15 × 3 × 0.5 = 22.5 J.

Work Done (W) = Force * Distance = 15 N * 3 m = 45 J.

Work done = Force × Distance = 15 N × 4 m = 60 J

Setting y = 0 in the equation gives 5x = 10, thus x = 2. The x-intercept is 2.

Setting y = 0 in the equation gives 5x + 10 = 0, thus x = -2.

Setting y = 0 in the equation gives 6x = 12, thus x = 2. The x-intercept is 2.

Rearranging gives y = (2/3)x + 2; y-intercept = 2

To find y-intercept, set x = 0: 2(0) - 3y = 6 => -3y = 6 => y = -2

Setting x = 0, we get -2y = 6, so y = -3.

Set x = 0: -2y = 6 => y = -3, y-intercept is 3.