Answer:
Wnet, in, = 133.33J
Explanation:
Provided that
Pump heat QH = 1000J
Hot temperature TH= 300K
Cold temperature TL= 260K
Given the heat pump is entirely reversible, the performance coefficient expression is formulated as follows:
According to the first law of thermodynamics,
COP(HP, rev) = 1/(1-TL/TH)
COP(HP, rev) = 1/(1-260/300)
COP(HP, rev) = 1/(1-0.867)
COP(HP, rev) = 1/0.133
COP(HP, rev) = 7.5
The power necessary to operate the heat pump is given by
Wnet, in = QH/COP(HP, rev)
Wnet, in = 1000/7.5
Wnet, in = 133.333J. QED
Thus, the 133.33J represents the initial work input during the heat transfer process.
<padditionally...><pbased on="" the="" first="" law="" rate="" at="" which="" heat="" is="" extracted="" from="" lower="" temperature="" reservoir="" calculated="" as="">
QL=QH-Wnet, in
QL=1000-133.333
QL=866.67J
</pbased></padditionally...>
Δd = 23 cm. When the eta string of the guitar has nodes at both ends, the resulting waves create a standing wave, which can be expressed with the following formulas: Fundamental: L = ½ λ, 1st harmonic: L = 2 ( λ / 2), 2nd harmonic: L = 3 ( λ / 2), Harmonic n: L = n λ / 2, where n is an integer. The rope's speed can be calculated using the formula v = λ f. This speed remains constant based on the tension and linear density of the rope. Now, let's determine the speed with the provided data: v = 0.69 × 196, yielding v = 135.24 m/s. Next, we will find the wavelengths for the two frequencies: λ₁ = v / f₁, which gives λ₁ = 135.24 / 233.08, equaling λ₁ = 0.58022 m; λ₂ = v / f₂ results in λ₂ = 135.24 / 246.94, consequently λ₂ = 0.54766 m. We'll substitute into the resonance equation Lₙ = n λ/2. At the third fret, m = 3, therefore L₃ = 3 × 0.58022 / 2, resulting in L₃ = 0.87033 m. For the fourth fret, m = 4, which gives L₄ = 4 × 0.54766 / 2, equating to L₄ = 1.09532 m. The distance between the two frets is Δd = L₄ – L₃, so Δd = 1.09532 - 0.87033, leading to Δd = 0.22499 m or 22.5 cm, rounded to 23 cm.
Answer:
Induced EMF is 2 x 10⁻³ volts
Explanation:
B = strength of the magnetic field aligning with the loop's axis = 1 T
= area change rate of the loop = 20 cm²/s = 20 x 10⁻⁴ m²
θ = the angle formed by the magnetic field and area vector = 0
E = the induced EMF across the loop
EMF can be calculated using the formula
E = B
E = (1) (20 x 10⁻⁴ )
E = 2 x 10⁻³ volts
E = 2 mV
